analysis.inner_product_space.linear_pmap ⟷ Mathlib.Analysis.InnerProductSpace.LinearPMap

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 -/
 import Analysis.InnerProductSpace.Adjoint
-import Topology.Algebra.Module.LinearPmap
+import Topology.Algebra.Module.LinearPMap
 import Topology.Algebra.Module.Basic
 
 #align_import analysis.inner_product_space.linear_pmap from "leanprover-community/mathlib"@"9240e8be927a0955b9a82c6c85ef499ee3a626b8"
@@ -54,11 +54,11 @@ Unbounded operators, closed operators
 
 noncomputable section
 
-open IsROrC
+open RCLike
 
 open scoped ComplexConjugate Classical
 
-variable {𝕜 E F G : Type _} [IsROrC 𝕜]
+variable {𝕜 E F G : Type _} [RCLike 𝕜]
 
 variable [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -105,39 +105,39 @@ def adjointDomain : Submodule 𝕜 F
 #align linear_pmap.adjoint_domain LinearPMap.adjointDomain
 -/
 
-#print LinearPMap.adjointDomainMkClm /-
+#print LinearPMap.adjointDomainMkCLM /-
 /-- The operator `λ x, ⟪y, T x⟫` considered as a continuous linear operator from `T.adjoint_domain`
 to `𝕜`. -/
-def adjointDomainMkClm (y : T.adjointDomain) : T.domain →L[𝕜] 𝕜 :=
+def adjointDomainMkCLM (y : T.adjointDomain) : T.domain →L[𝕜] 𝕜 :=
   ⟨(innerₛₗ 𝕜 (y : F)).comp T.toFun, y.Prop⟩
-#align linear_pmap.adjoint_domain_mk_clm LinearPMap.adjointDomainMkClm
+#align linear_pmap.adjoint_domain_mk_clm LinearPMap.adjointDomainMkCLM
 -/
 
-#print LinearPMap.adjointDomainMkClm_apply /-
-theorem adjointDomainMkClm_apply (y : T.adjointDomain) (x : T.domain) :
-    adjointDomainMkClm T y x = ⟪(y : F), T x⟫ :=
+#print LinearPMap.adjointDomainMkCLM_apply /-
+theorem adjointDomainMkCLM_apply (y : T.adjointDomain) (x : T.domain) :
+    adjointDomainMkCLM T y x = ⟪(y : F), T x⟫ :=
   rfl
-#align linear_pmap.adjoint_domain_mk_clm_apply LinearPMap.adjointDomainMkClm_apply
+#align linear_pmap.adjoint_domain_mk_clm_apply LinearPMap.adjointDomainMkCLM_apply
 -/
 
 variable {T}
 
 variable (hT : Dense (T.domain : Set E))
 
-#print LinearPMap.adjointDomainMkClmExtend /-
+#print LinearPMap.adjointDomainMkCLMExtend /-
 /-- The unique continuous extension of the operator `adjoint_domain_mk_clm` to `E`. -/
-def adjointDomainMkClmExtend (y : T.adjointDomain) : E →L[𝕜] 𝕜 :=
-  (T.adjointDomainMkClm y).extend (Submodule.subtypeL T.domain) hT.denseRange_val
+def adjointDomainMkCLMExtend (y : T.adjointDomain) : E →L[𝕜] 𝕜 :=
+  (T.adjointDomainMkCLM y).extend (Submodule.subtypeL T.domain) hT.denseRange_val
     uniformEmbedding_subtype_val.to_uniformInducing
-#align linear_pmap.adjoint_domain_mk_clm_extend LinearPMap.adjointDomainMkClmExtend
+#align linear_pmap.adjoint_domain_mk_clm_extend LinearPMap.adjointDomainMkCLMExtend
 -/
 
-#print LinearPMap.adjointDomainMkClmExtend_apply /-
+#print LinearPMap.adjointDomainMkCLMExtend_apply /-
 @[simp]
-theorem adjointDomainMkClmExtend_apply (y : T.adjointDomain) (x : T.domain) :
-    adjointDomainMkClmExtend hT y (x : E) = ⟪(y : F), T x⟫ :=
+theorem adjointDomainMkCLMExtend_apply (y : T.adjointDomain) (x : T.domain) :
+    adjointDomainMkCLMExtend hT y (x : E) = ⟪(y : F), T x⟫ :=
   ContinuousLinearMap.extend_eq _ _ _ _ _
-#align linear_pmap.adjoint_domain_mk_clm_extend_apply LinearPMap.adjointDomainMkClmExtend_apply
+#align linear_pmap.adjoint_domain_mk_clm_extend_apply LinearPMap.adjointDomainMkCLMExtend_apply
 -/
 
 variable [CompleteSpace E]
@@ -149,7 +149,7 @@ This is an auxiliary definition needed to define the adjoint operator as a `line
 the assumption that `T.domain` is dense. -/
 def adjointAux : T.adjointDomain →ₗ[𝕜] E
     where
-  toFun y := (InnerProductSpace.toDual 𝕜 E).symm (adjointDomainMkClmExtend hT y)
+  toFun y := (InnerProductSpace.toDual 𝕜 E).symm (adjointDomainMkCLMExtend hT y)
   map_add' x y :=
     hT.eq_of_inner_left fun _ => by
       simp only [inner_add_left, Submodule.coe_add, InnerProductSpace.toDual_symm_apply,

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,9 +3,9 @@ Copyright (c) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 -/
-import Mathbin.Analysis.InnerProductSpace.Adjoint
-import Mathbin.Topology.Algebra.Module.LinearPmap
-import Mathbin.Topology.Algebra.Module.Basic
+import Analysis.InnerProductSpace.Adjoint
+import Topology.Algebra.Module.LinearPmap
+import Topology.Algebra.Module.Basic
 
 #align_import analysis.inner_product_space.linear_pmap from "leanprover-community/mathlib"@"9240e8be927a0955b9a82c6c85ef499ee3a626b8"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
-
-! This file was ported from Lean 3 source module analysis.inner_product_space.linear_pmap
-! leanprover-community/mathlib commit 9240e8be927a0955b9a82c6c85ef499ee3a626b8
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.InnerProductSpace.Adjoint
 import Mathbin.Topology.Algebra.Module.LinearPmap
 import Mathbin.Topology.Algebra.Module.Basic
 
+#align_import analysis.inner_product_space.linear_pmap from "leanprover-community/mathlib"@"9240e8be927a0955b9a82c6c85ef499ee3a626b8"
+
 /-!
 
 # Partially defined linear operators on Hilbert spaces

mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.linear_pmap
-! leanprover-community/mathlib commit 8b981918a93bc45a8600de608cde7944a80d92b9
+! leanprover-community/mathlib commit 9240e8be927a0955b9a82c6c85ef499ee3a626b8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Topology.Algebra.Module.Basic
 
 # Partially defined linear operators on Hilbert spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We will develop the basics of the theory of unbounded operators on Hilbert spaces.
 
 ## Main definitions

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9

@@ -68,21 +68,26 @@ local notation "⟪" x ", " y "⟫" => @inner 𝕜 _ _ x y
 
 namespace LinearPMap
 
+#print LinearPMap.IsFormalAdjoint /-
 /-- An operator `T` is a formal adjoint of `S` if for all `x` in the domain of `T` and `y` in the
 domain of `S`, we have that `⟪T x, y⟫ = ⟪x, S y⟫`. -/
 def IsFormalAdjoint (T : E →ₗ.[𝕜] F) (S : F →ₗ.[𝕜] E) : Prop :=
   ∀ (x : T.domain) (y : S.domain), ⟪T x, y⟫ = ⟪(x : E), S y⟫
 #align linear_pmap.is_formal_adjoint LinearPMap.IsFormalAdjoint
+-/
 
 variable {T : E →ₗ.[𝕜] F} {S : F →ₗ.[𝕜] E}
 
+#print LinearPMap.IsFormalAdjoint.symm /-
 @[protected]
 theorem IsFormalAdjoint.symm (h : T.IsFormalAdjoint S) : S.IsFormalAdjoint T := fun y _ => by
   rw [← inner_conj_symm, ← inner_conj_symm (y : F), h]
 #align linear_pmap.is_formal_adjoint.symm LinearPMap.IsFormalAdjoint.symm
+-/
 
 variable (T)
 
+#print LinearPMap.adjointDomain /-
 /-- The domain of the adjoint operator.
 
 This definition is needed to construct the adjoint operator and the preferred version to use is
@@ -98,36 +103,46 @@ def adjointDomain : Submodule 𝕜 F
     rw [Set.mem_setOf_eq, LinearMap.map_smulₛₗ] at *
     exact hx.const_smul (conj a)
 #align linear_pmap.adjoint_domain LinearPMap.adjointDomain
+-/
 
+#print LinearPMap.adjointDomainMkClm /-
 /-- The operator `λ x, ⟪y, T x⟫` considered as a continuous linear operator from `T.adjoint_domain`
 to `𝕜`. -/
 def adjointDomainMkClm (y : T.adjointDomain) : T.domain →L[𝕜] 𝕜 :=
   ⟨(innerₛₗ 𝕜 (y : F)).comp T.toFun, y.Prop⟩
 #align linear_pmap.adjoint_domain_mk_clm LinearPMap.adjointDomainMkClm
+-/
 
+#print LinearPMap.adjointDomainMkClm_apply /-
 theorem adjointDomainMkClm_apply (y : T.adjointDomain) (x : T.domain) :
     adjointDomainMkClm T y x = ⟪(y : F), T x⟫ :=
   rfl
 #align linear_pmap.adjoint_domain_mk_clm_apply LinearPMap.adjointDomainMkClm_apply
+-/
 
 variable {T}
 
 variable (hT : Dense (T.domain : Set E))
 
+#print LinearPMap.adjointDomainMkClmExtend /-
 /-- The unique continuous extension of the operator `adjoint_domain_mk_clm` to `E`. -/
 def adjointDomainMkClmExtend (y : T.adjointDomain) : E →L[𝕜] 𝕜 :=
   (T.adjointDomainMkClm y).extend (Submodule.subtypeL T.domain) hT.denseRange_val
     uniformEmbedding_subtype_val.to_uniformInducing
 #align linear_pmap.adjoint_domain_mk_clm_extend LinearPMap.adjointDomainMkClmExtend
+-/
 
+#print LinearPMap.adjointDomainMkClmExtend_apply /-
 @[simp]
 theorem adjointDomainMkClmExtend_apply (y : T.adjointDomain) (x : T.domain) :
     adjointDomainMkClmExtend hT y (x : E) = ⟪(y : F), T x⟫ :=
   ContinuousLinearMap.extend_eq _ _ _ _ _
 #align linear_pmap.adjoint_domain_mk_clm_extend_apply LinearPMap.adjointDomainMkClmExtend_apply
+-/
 
 variable [CompleteSpace E]
 
+#print LinearPMap.adjointAux /-
 /-- The adjoint as a linear map from its domain to `E`.
 
 This is an auxiliary definition needed to define the adjoint operator as a `linear_pmap` without
@@ -144,34 +159,44 @@ def adjointAux : T.adjointDomain →ₗ[𝕜] E
       simp only [inner_smul_left, Submodule.coe_smul_of_tower, RingHom.id_apply,
         InnerProductSpace.toDual_symm_apply, adjoint_domain_mk_clm_extend_apply]
 #align linear_pmap.adjoint_aux LinearPMap.adjointAux
+-/
 
+#print LinearPMap.adjointAux_inner /-
 theorem adjointAux_inner (y : T.adjointDomain) (x : T.domain) :
     ⟪adjointAux hT y, x⟫ = ⟪(y : F), T x⟫ := by
   simp only [adjoint_aux, LinearMap.coe_mk, InnerProductSpace.toDual_symm_apply,
     adjoint_domain_mk_clm_extend_apply]
 #align linear_pmap.adjoint_aux_inner LinearPMap.adjointAux_inner
+-/
 
+#print LinearPMap.adjointAux_unique /-
 theorem adjointAux_unique (y : T.adjointDomain) {x₀ : E}
     (hx₀ : ∀ x : T.domain, ⟪x₀, x⟫ = ⟪(y : F), T x⟫) : adjointAux hT y = x₀ :=
   hT.eq_of_inner_left fun v => (adjointAux_inner hT _ _).trans (hx₀ v).symm
 #align linear_pmap.adjoint_aux_unique LinearPMap.adjointAux_unique
+-/
 
 variable (T)
 
+#print LinearPMap.adjoint /-
 /-- The adjoint operator as a partially defined linear operator. -/
 def adjoint : F →ₗ.[𝕜] E where
   domain := T.adjointDomain
   toFun := if hT : Dense (T.domain : Set E) then adjointAux hT else 0
 #align linear_pmap.adjoint LinearPMap.adjoint
+-/
 
 scoped postfix:1024 "†" => LinearPMap.adjoint
 
+#print LinearPMap.mem_adjoint_domain_iff /-
 theorem mem_adjoint_domain_iff (y : F) : y ∈ T†.domain ↔ Continuous ((innerₛₗ 𝕜 y).comp T.toFun) :=
   Iff.rfl
 #align linear_pmap.mem_adjoint_domain_iff LinearPMap.mem_adjoint_domain_iff
+-/
 
 variable {T}
 
+#print LinearPMap.mem_adjoint_domain_of_exists /-
 theorem mem_adjoint_domain_of_exists (y : F) (h : ∃ w : E, ∀ x : T.domain, ⟪w, x⟫ = ⟪y, T x⟫) :
     y ∈ T†.domain := by
   cases' h with w hw
@@ -180,29 +205,39 @@ theorem mem_adjoint_domain_of_exists (y : F) (h : ∃ w : E, ∀ x : T.domain, 
   convert this using 1
   exact funext fun x => (hw x).symm
 #align linear_pmap.mem_adjoint_domain_of_exists LinearPMap.mem_adjoint_domain_of_exists
+-/
 
+#print LinearPMap.adjoint_apply_of_not_dense /-
 theorem adjoint_apply_of_not_dense (hT : ¬Dense (T.domain : Set E)) (y : T†.domain) : T† y = 0 :=
   by
   change (if hT : Dense (T.domain : Set E) then adjoint_aux hT else 0) y = _
   simp only [hT, not_false_iff, dif_neg, LinearMap.zero_apply]
 #align linear_pmap.adjoint_apply_of_not_dense LinearPMap.adjoint_apply_of_not_dense
+-/
 
+#print LinearPMap.adjoint_apply_of_dense /-
 theorem adjoint_apply_of_dense (y : T†.domain) : T† y = adjointAux hT y :=
   by
   change (if hT : Dense (T.domain : Set E) then adjoint_aux hT else 0) y = _
   simp only [hT, dif_pos, LinearMap.coe_mk]
 #align linear_pmap.adjoint_apply_of_dense LinearPMap.adjoint_apply_of_dense
+-/
 
+#print LinearPMap.adjoint_apply_eq /-
 theorem adjoint_apply_eq (y : T†.domain) {x₀ : E} (hx₀ : ∀ x : T.domain, ⟪x₀, x⟫ = ⟪(y : F), T x⟫) :
     T† y = x₀ :=
   (adjoint_apply_of_dense hT y).symm ▸ adjointAux_unique hT _ hx₀
 #align linear_pmap.adjoint_apply_eq LinearPMap.adjoint_apply_eq
+-/
 
+#print LinearPMap.adjoint_isFormalAdjoint /-
 /-- The fundamental property of the adjoint. -/
 theorem adjoint_isFormalAdjoint : T†.IsFormalAdjoint T := fun x =>
   (adjoint_apply_of_dense hT x).symm ▸ adjointAux_inner hT x
 #align linear_pmap.adjoint_is_formal_adjoint LinearPMap.adjoint_isFormalAdjoint
+-/
 
+#print LinearPMap.IsFormalAdjoint.le_adjoint /-
 /-- The adjoint is maximal in the sense that it contains every formal adjoint. -/
 theorem IsFormalAdjoint.le_adjoint (h : T.IsFormalAdjoint S) : S ≤ T† :=
   ⟨-- Trivially, every `x : S.domain` is in `T.adjoint.domain`
@@ -212,6 +247,7 @@ theorem IsFormalAdjoint.le_adjoint (h : T.IsFormalAdjoint S) : S ≤ T† :=
   -- `⟪v, S x⟫ = ⟪v, T.adjoint y⟫` for all `v : T.domain`:
   fun _ _ hxy => (adjoint_apply_eq hT _ fun _ => by rw [h.symm, hxy]).symm⟩
 #align linear_pmap.is_formal_adjoint.le_adjoint LinearPMap.IsFormalAdjoint.le_adjoint
+-/
 
 end LinearPMap
 
@@ -221,6 +257,7 @@ variable [CompleteSpace E] [CompleteSpace F]
 
 variable (A : E →L[𝕜] F) {p : Submodule 𝕜 E}
 
+#print ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense /-
 /-- Restricting `A` to a dense submodule and taking the `linear_pmap.adjoint` is the same
 as taking the `continuous_linear_map.adjoint` interpreted as a `linear_pmap`. -/
 theorem toPMap_adjoint_eq_adjoint_toPMap_of_dense (hp : Dense (p : Set E)) :
@@ -234,6 +271,7 @@ theorem toPMap_adjoint_eq_adjoint_toPMap_of_dense (hp : Dense (p : Set E)) :
   refine' LinearPMap.adjoint_apply_eq hp _ fun v => _
   simp only [adjoint_inner_left, hxy, LinearMap.toPMap_apply, to_linear_map_eq_coe, coe_coe]
 #align continuous_linear_map.to_pmap_adjoint_eq_adjoint_to_pmap_of_dense ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense
+-/
 
 end ContinuousLinearMap
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9

@@ -216,7 +216,7 @@ variable [CompleteSpace E] [CompleteSpace F]
 variable (A : E →L[𝕜] F) {p : Submodule 𝕜 E}
 
 /-- Restricting `A` to a dense submodule and taking the `LinearPMap.adjoint` is the same
-as taking the `continuous_linear_map.adjoint` interpreted as a `linear_pmap`. -/
+as taking the `ContinuousLinearMap.adjoint` interpreted as a `LinearPMap`. -/
 theorem toPMap_adjoint_eq_adjoint_toPMap_of_dense (hp : Dense (p : Set E)) :
     (A.toPMap p).adjoint = A.adjoint.toPMap ⊤ := by
   ext x y hxy

IsROrC contains data, which goes against the expectation that classes prefixed with Is are prop-valued. People have been complaining about this on and off, so this PR renames IsROrC to RCLike.

@@ -50,11 +50,11 @@ Unbounded operators, closed operators
 
 noncomputable section
 
-open IsROrC
+open RCLike
 
 open scoped ComplexConjugate Classical
 
-variable {𝕜 E F G : Type*} [IsROrC 𝕜]
+variable {𝕜 E F G : Type*} [RCLike 𝕜]
 variable [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
 variable [NormedAddCommGroup F] [InnerProductSpace 𝕜 F]
 

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -55,9 +55,7 @@ open IsROrC
 open scoped ComplexConjugate Classical
 
 variable {𝕜 E F G : Type*} [IsROrC 𝕜]
-
 variable [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
-
 variable [NormedAddCommGroup F] [InnerProductSpace 𝕜 F]
 
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 _ _ x y
@@ -107,7 +105,6 @@ theorem adjointDomainMkCLM_apply (y : T.adjointDomain) (x : T.domain) :
 #align linear_pmap.adjoint_domain_mk_clm_apply LinearPMap.adjointDomainMkCLM_apply
 
 variable {T}
-
 variable (hT : Dense (T.domain : Set E))
 
 /-- The unique continuous extension of the operator `adjointDomainMkCLM` to `E`. -/
@@ -216,7 +213,6 @@ end LinearPMap
 namespace ContinuousLinearMap
 
 variable [CompleteSpace E] [CompleteSpace F]
-
 variable (A : E →L[𝕜] F) {p : Submodule 𝕜 E}
 
 /-- Restricting `A` to a dense submodule and taking the `LinearPMap.adjoint` is the same

Use Lean 4 syntax fun x ↦ instead, matching the style guide. This is close to exhaustive for doc comments; mathlib has about 460 remaining uses of λ (not all in Lean 3 syntax).

@@ -95,8 +95,8 @@ def adjointDomain : Submodule 𝕜 F where
     exact hx.const_smul (conj a)
 #align linear_pmap.adjoint_domain LinearPMap.adjointDomain
 
-/-- The operator `λ x, ⟪y, T x⟫` considered as a continuous linear operator from `T.adjointDomain`
-to `𝕜`. -/
+/-- The operator `fun x ↦ ⟪y, T x⟫` considered as a continuous linear operator
+from `T.adjointDomain` to `𝕜`. -/
 def adjointDomainMkCLM (y : T.adjointDomain) : T.domain →L[𝕜] 𝕜 :=
   ⟨(innerₛₗ 𝕜 (y : F)).comp T.toFun, y.prop⟩
 #align linear_pmap.adjoint_domain_mk_clm LinearPMap.adjointDomainMkCLM

Rename

• Complex.equivRealProdClm → Complex.equivRealProdCLM;
  • TODO: should this one use CLE?
• Complex.reClm → Complex.reCLM;
• Complex.imClm → Complex.imCLM;
• Complex.conjLie → Complex.conjLIE;
• Complex.conjCle → Complex.conjCLE;
• Complex.ofRealLi → Complex.ofRealLI;
• Complex.ofRealClm → Complex.ofRealCLM;
• fderivInnerClm → fderivInnerCLM;
• LinearPMap.adjointDomainMkClm → LinearPMap.adjointDomainMkCLM;
• LinearPMap.adjointDomainMkClmExtend → LinearPMap.adjointDomainMkCLMExtend;
• IsROrC.reClm → IsROrC.reCLM;
• IsROrC.imClm → IsROrC.imCLM;
• IsROrC.conjLie → IsROrC.conjLIE;
• IsROrC.conjCle → IsROrC.conjCLE;
• IsROrC.ofRealLi → IsROrC.ofRealLI;
• IsROrC.ofRealClm → IsROrC.ofRealCLM;
• MeasureTheory.condexpL1Clm → MeasureTheory.condexpL1CLM;
• algebraMapClm → algebraMapCLM;
• WeakDual.CharacterSpace.toClm → WeakDual.CharacterSpace.toCLM;
• BoundedContinuousFunction.evalClm → BoundedContinuousFunction.evalCLM;
• ContinuousMap.evalClm → ContinuousMap.evalCLM;
• TrivSqZeroExt.fstClm → TrivSqZeroExt.fstClm;
• TrivSqZeroExt.sndClm → TrivSqZeroExt.sndCLM;
• TrivSqZeroExt.inlClm → TrivSqZeroExt.inlCLM;
• TrivSqZeroExt.inrClm → TrivSqZeroExt.inrCLM

and related theorems.

@@ -97,30 +97,30 @@ def adjointDomain : Submodule 𝕜 F where
 
 /-- The operator `λ x, ⟪y, T x⟫` considered as a continuous linear operator from `T.adjointDomain`
 to `𝕜`. -/
-def adjointDomainMkClm (y : T.adjointDomain) : T.domain →L[𝕜] 𝕜 :=
+def adjointDomainMkCLM (y : T.adjointDomain) : T.domain →L[𝕜] 𝕜 :=
   ⟨(innerₛₗ 𝕜 (y : F)).comp T.toFun, y.prop⟩
-#align linear_pmap.adjoint_domain_mk_clm LinearPMap.adjointDomainMkClm
+#align linear_pmap.adjoint_domain_mk_clm LinearPMap.adjointDomainMkCLM
 
-theorem adjointDomainMkClm_apply (y : T.adjointDomain) (x : T.domain) :
-    adjointDomainMkClm T y x = ⟪(y : F), T x⟫ :=
+theorem adjointDomainMkCLM_apply (y : T.adjointDomain) (x : T.domain) :
+    adjointDomainMkCLM T y x = ⟪(y : F), T x⟫ :=
   rfl
-#align linear_pmap.adjoint_domain_mk_clm_apply LinearPMap.adjointDomainMkClm_apply
+#align linear_pmap.adjoint_domain_mk_clm_apply LinearPMap.adjointDomainMkCLM_apply
 
 variable {T}
 
 variable (hT : Dense (T.domain : Set E))
 
-/-- The unique continuous extension of the operator `adjointDomainMkClm` to `E`. -/
-def adjointDomainMkClmExtend (y : T.adjointDomain) : E →L[𝕜] 𝕜 :=
-  (T.adjointDomainMkClm y).extend (Submodule.subtypeL T.domain) hT.denseRange_val
+/-- The unique continuous extension of the operator `adjointDomainMkCLM` to `E`. -/
+def adjointDomainMkCLMExtend (y : T.adjointDomain) : E →L[𝕜] 𝕜 :=
+  (T.adjointDomainMkCLM y).extend (Submodule.subtypeL T.domain) hT.denseRange_val
     uniformEmbedding_subtype_val.toUniformInducing
-#align linear_pmap.adjoint_domain_mk_clm_extend LinearPMap.adjointDomainMkClmExtend
+#align linear_pmap.adjoint_domain_mk_clm_extend LinearPMap.adjointDomainMkCLMExtend
 
 @[simp]
-theorem adjointDomainMkClmExtend_apply (y : T.adjointDomain) (x : T.domain) :
-    adjointDomainMkClmExtend hT y (x : E) = ⟪(y : F), T x⟫ :=
+theorem adjointDomainMkCLMExtend_apply (y : T.adjointDomain) (x : T.domain) :
+    adjointDomainMkCLMExtend hT y (x : E) = ⟪(y : F), T x⟫ :=
   ContinuousLinearMap.extend_eq _ _ _ _ _
-#align linear_pmap.adjoint_domain_mk_clm_extend_apply LinearPMap.adjointDomainMkClmExtend_apply
+#align linear_pmap.adjoint_domain_mk_clm_extend_apply LinearPMap.adjointDomainMkCLMExtend_apply
 
 variable [CompleteSpace E]
 
@@ -129,25 +129,25 @@ variable [CompleteSpace E]
 This is an auxiliary definition needed to define the adjoint operator as a `LinearPMap` without
 the assumption that `T.domain` is dense. -/
 def adjointAux : T.adjointDomain →ₗ[𝕜] E where
-  toFun y := (InnerProductSpace.toDual 𝕜 E).symm (adjointDomainMkClmExtend hT y)
+  toFun y := (InnerProductSpace.toDual 𝕜 E).symm (adjointDomainMkCLMExtend hT y)
   map_add' x y :=
     hT.eq_of_inner_left fun _ => by
       simp only [inner_add_left, Submodule.coe_add, InnerProductSpace.toDual_symm_apply,
-        adjointDomainMkClmExtend_apply]
+        adjointDomainMkCLMExtend_apply]
   map_smul' _ _ :=
     hT.eq_of_inner_left fun _ => by
       simp only [inner_smul_left, Submodule.coe_smul_of_tower, RingHom.id_apply,
-        InnerProductSpace.toDual_symm_apply, adjointDomainMkClmExtend_apply]
+        InnerProductSpace.toDual_symm_apply, adjointDomainMkCLMExtend_apply]
 #align linear_pmap.adjoint_aux LinearPMap.adjointAux
 
 theorem adjointAux_inner (y : T.adjointDomain) (x : T.domain) :
     ⟪adjointAux hT y, x⟫ = ⟪(y : F), T x⟫ := by
   simp only [adjointAux, LinearMap.coe_mk, InnerProductSpace.toDual_symm_apply,
-    adjointDomainMkClmExtend_apply]
+    adjointDomainMkCLMExtend_apply]
   -- Porting note(https://github.com/leanprover-community/mathlib4/issues/5026):
   -- mathlib3 was finished here
   simp only [AddHom.coe_mk, InnerProductSpace.toDual_symm_apply]
-  rw [adjointDomainMkClmExtend_apply]
+  rw [adjointDomainMkCLMExtend_apply]
 #align linear_pmap.adjoint_aux_inner LinearPMap.adjointAux_inner
 
 theorem adjointAux_unique (y : T.adjointDomain) {x₀ : E}

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -4,7 +4,6 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 -/
 import Mathlib.Analysis.InnerProductSpace.Adjoint
-import Mathlib.Topology.Algebra.Module.LinearPMap
 import Mathlib.Topology.Algebra.Module.Basic
 
 #align_import analysis.inner_product_space.linear_pmap from "leanprover-community/mathlib"@"8b981918a93bc45a8600de608cde7944a80d92b9"

This reverts commit f3695eb2.

@@ -4,7 +4,6 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 -/
 import Mathlib.Analysis.InnerProductSpace.Adjoint
-import Mathlib.Analysis.InnerProductSpace.ProdL2
 import Mathlib.Topology.Algebra.Module.LinearPMap
 import Mathlib.Topology.Algebra.Module.Basic
 
@@ -28,8 +27,6 @@ We will develop the basics of the theory of unbounded operators on Hilbert space
 * `LinearPMap.IsFormalAdjoint.le_adjoint`: Every formal adjoint is contained in the adjoint
 * `ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense`: The adjoint on
   `ContinuousLinearMap` and `LinearPMap` coincide.
-* `LinearPMap.adjoint_isClosed`: The adjoint is a closed operator.
-* `IsSelfAdjoint.isClosed`: Every self-adjoint operator is closed.
 
 ## Notation
 
@@ -54,7 +51,7 @@ Unbounded operators, closed operators
 
 noncomputable section
 
-open IsROrC LinearPMap
+open IsROrC
 
 open scoped ComplexConjugate Classical
 
@@ -271,93 +268,3 @@ theorem _root_.IsSelfAdjoint.dense_domain (hA : IsSelfAdjoint A) : Dense (A.doma
 end LinearPMap
 
 end Star
-
-/-! ### The graph of the adjoint -/
-
-namespace Submodule
-
-/-- The adjoint of a submodule
-
-Note that the adjoint is taken with respect to the L^2 inner product on `E × F`, which is defined
-as `WithLp 2 (E × F)`. -/
-protected noncomputable
-def adjoint (g : Submodule 𝕜 (E × F)) : Submodule 𝕜 (F × E) :=
-    (g.map <| (LinearEquiv.skewSwap 𝕜 F E).symm.trans
-      (WithLp.linearEquiv 2 𝕜 (F × E)).symm).orthogonal.map (WithLp.linearEquiv 2 𝕜 (F × E))
-
-@[simp]
-theorem mem_adjoint_iff (g : Submodule 𝕜 (E × F)) (x : F × E) :
-    x ∈ g.adjoint ↔
-    ∀ a b, (a, b) ∈ g → inner (𝕜 := 𝕜) b x.fst - inner a x.snd = 0 := by
-  simp only [Submodule.adjoint, Submodule.mem_map, Submodule.mem_orthogonal, LinearMap.coe_comp,
-    LinearEquiv.coe_coe, WithLp.linearEquiv_symm_apply, Function.comp_apply,
-    LinearEquiv.skewSwap_symm_apply, Prod.exists, WithLp.prod_inner_apply, forall_exists_index,
-    and_imp, WithLp.linearEquiv_apply]
-  constructor
-  · rintro ⟨y, h1, h2⟩ a b hab
-    rw [← h2, WithLp.equiv_fst, WithLp.equiv_snd]
-    specialize h1 (b, -a) a b hab rfl
-    simp only [inner_neg_left, ← sub_eq_add_neg] at h1
-    exact h1
-  · intro h
-    refine ⟨x, ?_, rfl⟩
-    intro u a b hab hu
-    simp [← hu, ← sub_eq_add_neg, h a b hab]
-
-variable {T : E →ₗ.[𝕜] F} [CompleteSpace E]
-
-theorem _root_.LinearPMap.adjoint_graph_eq_graph_adjoint (hT : Dense (T.domain : Set E)) :
-    T†.graph = T.graph.adjoint := by
-  ext x
-  simp only [mem_graph_iff, Subtype.exists, exists_and_left, exists_eq_left, mem_adjoint_iff,
-    forall_exists_index, forall_apply_eq_imp_iff']
-  constructor
-  · rintro ⟨hx, h⟩ a ha
-    rw [← h, (adjoint_isFormalAdjoint hT).symm ⟨a, ha⟩ ⟨x.fst, hx⟩, sub_self]
-  · intro h
-    simp_rw [sub_eq_zero] at h
-    have hx : x.fst ∈ T†.domain
-    · apply mem_adjoint_domain_of_exists
-      use x.snd
-      rintro ⟨a, ha⟩
-      rw [← inner_conj_symm, ← h a ha, inner_conj_symm]
-    use hx
-    apply hT.eq_of_inner_right
-    rintro ⟨a, ha⟩
-    rw [← h a ha, (adjoint_isFormalAdjoint hT).symm ⟨a, ha⟩ ⟨x.fst, hx⟩]
-
-@[simp]
-theorem _root_.LinearPMap.graph_adjoint_toLinearPMap_eq_adjoint (hT : Dense (T.domain : Set E)) :
-    T.graph.adjoint.toLinearPMap = T† := by
-  apply eq_of_eq_graph
-  rw [adjoint_graph_eq_graph_adjoint hT]
-  apply Submodule.toLinearPMap_graph_eq
-  intro x hx hx'
-  simp only [mem_adjoint_iff, mem_graph_iff, Subtype.exists, exists_and_left, exists_eq_left,
-    forall_exists_index, forall_apply_eq_imp_iff', hx', inner_zero_right, zero_sub,
-    neg_eq_zero] at hx
-  apply hT.eq_zero_of_inner_right
-  rintro ⟨a, ha⟩
-  exact hx a ha
-
-end Submodule
-
-/-! ### Closedness -/
-
-namespace LinearPMap
-
-variable {T : E →ₗ.[𝕜] F} [CompleteSpace E]
-
-theorem adjoint_isClosed (hT : Dense (T.domain : Set E)) :
-    T†.IsClosed := by
-  rw [IsClosed, adjoint_graph_eq_graph_adjoint hT, Submodule.adjoint]
-  simp only [Submodule.map_coe, WithLp.linearEquiv_apply]
-  rw [Equiv.image_eq_preimage]
-  exact (Submodule.isClosed_orthogonal _).preimage (WithLp.prod_continuous_equiv_symm _ _ _)
-
-/-- Every self-adjoint `LinearPMap` is closed. -/
-theorem _root_.IsSelfAdjoint.isClosed {A : E →ₗ.[𝕜] E} (hA : IsSelfAdjoint A) : A.IsClosed := by
-  rw [← isSelfAdjoint_def.mp hA]
-  exact adjoint_isClosed hA.dense_domain
-
-end LinearPMap

This reverts commit 26eb2b0a.

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 -/
 import Mathlib.Analysis.InnerProductSpace.Adjoint
+import Mathlib.Analysis.InnerProductSpace.ProdL2
 import Mathlib.Topology.Algebra.Module.LinearPMap
 import Mathlib.Topology.Algebra.Module.Basic
 
@@ -27,6 +28,8 @@ We will develop the basics of the theory of unbounded operators on Hilbert space
 * `LinearPMap.IsFormalAdjoint.le_adjoint`: Every formal adjoint is contained in the adjoint
 * `ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense`: The adjoint on
   `ContinuousLinearMap` and `LinearPMap` coincide.
+* `LinearPMap.adjoint_isClosed`: The adjoint is a closed operator.
+* `IsSelfAdjoint.isClosed`: Every self-adjoint operator is closed.
 
 ## Notation
 
@@ -51,7 +54,7 @@ Unbounded operators, closed operators
 
 noncomputable section
 
-open IsROrC
+open IsROrC LinearPMap
 
 open scoped ComplexConjugate Classical
 
@@ -268,3 +271,93 @@ theorem _root_.IsSelfAdjoint.dense_domain (hA : IsSelfAdjoint A) : Dense (A.doma
 end LinearPMap
 
 end Star
+
+/-! ### The graph of the adjoint -/
+
+namespace Submodule
+
+/-- The adjoint of a submodule
+
+Note that the adjoint is taken with respect to the L^2 inner product on `E × F`, which is defined
+as `WithLp 2 (E × F)`. -/
+protected noncomputable
+def adjoint (g : Submodule 𝕜 (E × F)) : Submodule 𝕜 (F × E) :=
+    (g.map <| (LinearEquiv.skewSwap 𝕜 F E).symm.trans
+      (WithLp.linearEquiv 2 𝕜 (F × E)).symm).orthogonal.map (WithLp.linearEquiv 2 𝕜 (F × E))
+
+@[simp]
+theorem mem_adjoint_iff (g : Submodule 𝕜 (E × F)) (x : F × E) :
+    x ∈ g.adjoint ↔
+    ∀ a b, (a, b) ∈ g → inner (𝕜 := 𝕜) b x.fst - inner a x.snd = 0 := by
+  simp only [Submodule.adjoint, Submodule.mem_map, Submodule.mem_orthogonal, LinearMap.coe_comp,
+    LinearEquiv.coe_coe, WithLp.linearEquiv_symm_apply, Function.comp_apply,
+    LinearEquiv.skewSwap_symm_apply, Prod.exists, WithLp.prod_inner_apply, forall_exists_index,
+    and_imp, WithLp.linearEquiv_apply]
+  constructor
+  · rintro ⟨y, h1, h2⟩ a b hab
+    rw [← h2, WithLp.equiv_fst, WithLp.equiv_snd]
+    specialize h1 (b, -a) a b hab rfl
+    simp only [inner_neg_left, ← sub_eq_add_neg] at h1
+    exact h1
+  · intro h
+    refine ⟨x, ?_, rfl⟩
+    intro u a b hab hu
+    simp [← hu, ← sub_eq_add_neg, h a b hab]
+
+variable {T : E →ₗ.[𝕜] F} [CompleteSpace E]
+
+theorem _root_.LinearPMap.adjoint_graph_eq_graph_adjoint (hT : Dense (T.domain : Set E)) :
+    T†.graph = T.graph.adjoint := by
+  ext x
+  simp only [mem_graph_iff, Subtype.exists, exists_and_left, exists_eq_left, mem_adjoint_iff,
+    forall_exists_index, forall_apply_eq_imp_iff']
+  constructor
+  · rintro ⟨hx, h⟩ a ha
+    rw [← h, (adjoint_isFormalAdjoint hT).symm ⟨a, ha⟩ ⟨x.fst, hx⟩, sub_self]
+  · intro h
+    simp_rw [sub_eq_zero] at h
+    have hx : x.fst ∈ T†.domain
+    · apply mem_adjoint_domain_of_exists
+      use x.snd
+      rintro ⟨a, ha⟩
+      rw [← inner_conj_symm, ← h a ha, inner_conj_symm]
+    use hx
+    apply hT.eq_of_inner_right
+    rintro ⟨a, ha⟩
+    rw [← h a ha, (adjoint_isFormalAdjoint hT).symm ⟨a, ha⟩ ⟨x.fst, hx⟩]
+
+@[simp]
+theorem _root_.LinearPMap.graph_adjoint_toLinearPMap_eq_adjoint (hT : Dense (T.domain : Set E)) :
+    T.graph.adjoint.toLinearPMap = T† := by
+  apply eq_of_eq_graph
+  rw [adjoint_graph_eq_graph_adjoint hT]
+  apply Submodule.toLinearPMap_graph_eq
+  intro x hx hx'
+  simp only [mem_adjoint_iff, mem_graph_iff, Subtype.exists, exists_and_left, exists_eq_left,
+    forall_exists_index, forall_apply_eq_imp_iff', hx', inner_zero_right, zero_sub,
+    neg_eq_zero] at hx
+  apply hT.eq_zero_of_inner_right
+  rintro ⟨a, ha⟩
+  exact hx a ha
+
+end Submodule
+
+/-! ### Closedness -/
+
+namespace LinearPMap
+
+variable {T : E →ₗ.[𝕜] F} [CompleteSpace E]
+
+theorem adjoint_isClosed (hT : Dense (T.domain : Set E)) :
+    T†.IsClosed := by
+  rw [IsClosed, adjoint_graph_eq_graph_adjoint hT, Submodule.adjoint]
+  simp only [Submodule.map_coe, WithLp.linearEquiv_apply]
+  rw [Equiv.image_eq_preimage]
+  exact (Submodule.isClosed_orthogonal _).preimage (WithLp.prod_continuous_equiv_symm _ _ _)
+
+/-- Every self-adjoint `LinearPMap` is closed. -/
+theorem _root_.IsSelfAdjoint.isClosed {A : E →ₗ.[𝕜] E} (hA : IsSelfAdjoint A) : A.IsClosed := by
+  rw [← isSelfAdjoint_def.mp hA]
+  exact adjoint_isClosed hA.dense_domain
+
+end LinearPMap

This includes all the changes from #7606.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -4,7 +4,6 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 -/
 import Mathlib.Analysis.InnerProductSpace.Adjoint
-import Mathlib.Analysis.InnerProductSpace.ProdL2
 import Mathlib.Topology.Algebra.Module.LinearPMap
 import Mathlib.Topology.Algebra.Module.Basic
 
@@ -28,8 +27,6 @@ We will develop the basics of the theory of unbounded operators on Hilbert space
 * `LinearPMap.IsFormalAdjoint.le_adjoint`: Every formal adjoint is contained in the adjoint
 * `ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense`: The adjoint on
   `ContinuousLinearMap` and `LinearPMap` coincide.
-* `LinearPMap.adjoint_isClosed`: The adjoint is a closed operator.
-* `IsSelfAdjoint.isClosed`: Every self-adjoint operator is closed.
 
 ## Notation
 
@@ -54,7 +51,7 @@ Unbounded operators, closed operators
 
 noncomputable section
 
-open IsROrC LinearPMap
+open IsROrC
 
 open scoped ComplexConjugate Classical
 
@@ -271,93 +268,3 @@ theorem _root_.IsSelfAdjoint.dense_domain (hA : IsSelfAdjoint A) : Dense (A.doma
 end LinearPMap
 
 end Star
-
-/-! ### The graph of the adjoint -/
-
-namespace Submodule
-
-/-- The adjoint of a submodule
-
-Note that the adjoint is taken with respect to the L^2 inner product on `E × F`, which is defined
-as `WithLp 2 (E × F)`. -/
-protected noncomputable
-def adjoint (g : Submodule 𝕜 (E × F)) : Submodule 𝕜 (F × E) :=
-    (g.map <| (LinearEquiv.skewSwap 𝕜 F E).symm.trans
-      (WithLp.linearEquiv 2 𝕜 (F × E)).symm).orthogonal.map (WithLp.linearEquiv 2 𝕜 (F × E))
-
-@[simp]
-theorem mem_adjoint_iff (g : Submodule 𝕜 (E × F)) (x : F × E) :
-    x ∈ g.adjoint ↔
-    ∀ a b, (a, b) ∈ g → inner (𝕜 := 𝕜) b x.fst - inner a x.snd = 0 := by
-  simp only [Submodule.adjoint, Submodule.mem_map, Submodule.mem_orthogonal, LinearMap.coe_comp,
-    LinearEquiv.coe_coe, WithLp.linearEquiv_symm_apply, Function.comp_apply,
-    LinearEquiv.skewSwap_symm_apply, Prod.exists, WithLp.prod_inner_apply, forall_exists_index,
-    and_imp, WithLp.linearEquiv_apply]
-  constructor
-  · rintro ⟨y, h1, h2⟩ a b hab
-    rw [← h2, WithLp.equiv_fst, WithLp.equiv_snd]
-    specialize h1 (b, -a) a b hab rfl
-    simp only [inner_neg_left, ← sub_eq_add_neg] at h1
-    exact h1
-  · intro h
-    refine ⟨x, ?_, rfl⟩
-    intro u a b hab hu
-    simp [← hu, ← sub_eq_add_neg, h a b hab]
-
-variable {T : E →ₗ.[𝕜] F} [CompleteSpace E]
-
-theorem _root_.LinearPMap.adjoint_graph_eq_graph_adjoint (hT : Dense (T.domain : Set E)) :
-    T†.graph = T.graph.adjoint := by
-  ext x
-  simp only [mem_graph_iff, Subtype.exists, exists_and_left, exists_eq_left, mem_adjoint_iff,
-    forall_exists_index, forall_apply_eq_imp_iff']
-  constructor
-  · rintro ⟨hx, h⟩ a ha
-    rw [← h, (adjoint_isFormalAdjoint hT).symm ⟨a, ha⟩ ⟨x.fst, hx⟩, sub_self]
-  · intro h
-    simp_rw [sub_eq_zero] at h
-    have hx : x.fst ∈ T†.domain
-    · apply mem_adjoint_domain_of_exists
-      use x.snd
-      rintro ⟨a, ha⟩
-      rw [← inner_conj_symm, ← h a ha, inner_conj_symm]
-    use hx
-    apply hT.eq_of_inner_right
-    rintro ⟨a, ha⟩
-    rw [← h a ha, (adjoint_isFormalAdjoint hT).symm ⟨a, ha⟩ ⟨x.fst, hx⟩]
-
-@[simp]
-theorem _root_.LinearPMap.graph_adjoint_toLinearPMap_eq_adjoint (hT : Dense (T.domain : Set E)) :
-    T.graph.adjoint.toLinearPMap = T† := by
-  apply eq_of_eq_graph
-  rw [adjoint_graph_eq_graph_adjoint hT]
-  apply Submodule.toLinearPMap_graph_eq
-  intro x hx hx'
-  simp only [mem_adjoint_iff, mem_graph_iff, Subtype.exists, exists_and_left, exists_eq_left,
-    forall_exists_index, forall_apply_eq_imp_iff', hx', inner_zero_right, zero_sub,
-    neg_eq_zero] at hx
-  apply hT.eq_zero_of_inner_right
-  rintro ⟨a, ha⟩
-  exact hx a ha
-
-end Submodule
-
-/-! ### Closedness -/
-
-namespace LinearPMap
-
-variable {T : E →ₗ.[𝕜] F} [CompleteSpace E]
-
-theorem adjoint_isClosed (hT : Dense (T.domain : Set E)) :
-    T†.IsClosed := by
-  rw [IsClosed, adjoint_graph_eq_graph_adjoint hT, Submodule.adjoint]
-  simp only [Submodule.map_coe, WithLp.linearEquiv_apply]
-  rw [Equiv.image_eq_preimage]
-  exact (Submodule.isClosed_orthogonal _).preimage (WithLp.prod_continuous_equiv_symm _ _ _)
-
-/-- Every self-adjoint `LinearPMap` is closed. -/
-theorem _root_.IsSelfAdjoint.isClosed {A : E →ₗ.[𝕜] E} (hA : IsSelfAdjoint A) : A.IsClosed := by
-  rw [← isSelfAdjoint_def.mp hA]
-  exact adjoint_isClosed hA.dense_domain
-
-end LinearPMap

Define the graph of the adjoint and prove that the adjoint operator is always closed.

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 -/
 import Mathlib.Analysis.InnerProductSpace.Adjoint
+import Mathlib.Analysis.InnerProductSpace.ProdL2
 import Mathlib.Topology.Algebra.Module.LinearPMap
 import Mathlib.Topology.Algebra.Module.Basic
 
@@ -27,6 +28,8 @@ We will develop the basics of the theory of unbounded operators on Hilbert space
 * `LinearPMap.IsFormalAdjoint.le_adjoint`: Every formal adjoint is contained in the adjoint
 * `ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense`: The adjoint on
   `ContinuousLinearMap` and `LinearPMap` coincide.
+* `LinearPMap.adjoint_isClosed`: The adjoint is a closed operator.
+* `IsSelfAdjoint.isClosed`: Every self-adjoint operator is closed.
 
 ## Notation
 
@@ -51,7 +54,7 @@ Unbounded operators, closed operators
 
 noncomputable section
 
-open IsROrC
+open IsROrC LinearPMap
 
 open scoped ComplexConjugate Classical
 
@@ -268,3 +271,93 @@ theorem _root_.IsSelfAdjoint.dense_domain (hA : IsSelfAdjoint A) : Dense (A.doma
 end LinearPMap
 
 end Star
+
+/-! ### The graph of the adjoint -/
+
+namespace Submodule
+
+/-- The adjoint of a submodule
+
+Note that the adjoint is taken with respect to the L^2 inner product on `E × F`, which is defined
+as `WithLp 2 (E × F)`. -/
+protected noncomputable
+def adjoint (g : Submodule 𝕜 (E × F)) : Submodule 𝕜 (F × E) :=
+    (g.map <| (LinearEquiv.skewSwap 𝕜 F E).symm.trans
+      (WithLp.linearEquiv 2 𝕜 (F × E)).symm).orthogonal.map (WithLp.linearEquiv 2 𝕜 (F × E))
+
+@[simp]
+theorem mem_adjoint_iff (g : Submodule 𝕜 (E × F)) (x : F × E) :
+    x ∈ g.adjoint ↔
+    ∀ a b, (a, b) ∈ g → inner (𝕜 := 𝕜) b x.fst - inner a x.snd = 0 := by
+  simp only [Submodule.adjoint, Submodule.mem_map, Submodule.mem_orthogonal, LinearMap.coe_comp,
+    LinearEquiv.coe_coe, WithLp.linearEquiv_symm_apply, Function.comp_apply,
+    LinearEquiv.skewSwap_symm_apply, Prod.exists, WithLp.prod_inner_apply, forall_exists_index,
+    and_imp, WithLp.linearEquiv_apply]
+  constructor
+  · rintro ⟨y, h1, h2⟩ a b hab
+    rw [← h2, WithLp.equiv_fst, WithLp.equiv_snd]
+    specialize h1 (b, -a) a b hab rfl
+    simp only [inner_neg_left, ← sub_eq_add_neg] at h1
+    exact h1
+  · intro h
+    refine ⟨x, ?_, rfl⟩
+    intro u a b hab hu
+    simp [← hu, ← sub_eq_add_neg, h a b hab]
+
+variable {T : E →ₗ.[𝕜] F} [CompleteSpace E]
+
+theorem _root_.LinearPMap.adjoint_graph_eq_graph_adjoint (hT : Dense (T.domain : Set E)) :
+    T†.graph = T.graph.adjoint := by
+  ext x
+  simp only [mem_graph_iff, Subtype.exists, exists_and_left, exists_eq_left, mem_adjoint_iff,
+    forall_exists_index, forall_apply_eq_imp_iff']
+  constructor
+  · rintro ⟨hx, h⟩ a ha
+    rw [← h, (adjoint_isFormalAdjoint hT).symm ⟨a, ha⟩ ⟨x.fst, hx⟩, sub_self]
+  · intro h
+    simp_rw [sub_eq_zero] at h
+    have hx : x.fst ∈ T†.domain
+    · apply mem_adjoint_domain_of_exists
+      use x.snd
+      rintro ⟨a, ha⟩
+      rw [← inner_conj_symm, ← h a ha, inner_conj_symm]
+    use hx
+    apply hT.eq_of_inner_right
+    rintro ⟨a, ha⟩
+    rw [← h a ha, (adjoint_isFormalAdjoint hT).symm ⟨a, ha⟩ ⟨x.fst, hx⟩]
+
+@[simp]
+theorem _root_.LinearPMap.graph_adjoint_toLinearPMap_eq_adjoint (hT : Dense (T.domain : Set E)) :
+    T.graph.adjoint.toLinearPMap = T† := by
+  apply eq_of_eq_graph
+  rw [adjoint_graph_eq_graph_adjoint hT]
+  apply Submodule.toLinearPMap_graph_eq
+  intro x hx hx'
+  simp only [mem_adjoint_iff, mem_graph_iff, Subtype.exists, exists_and_left, exists_eq_left,
+    forall_exists_index, forall_apply_eq_imp_iff', hx', inner_zero_right, zero_sub,
+    neg_eq_zero] at hx
+  apply hT.eq_zero_of_inner_right
+  rintro ⟨a, ha⟩
+  exact hx a ha
+
+end Submodule
+
+/-! ### Closedness -/
+
+namespace LinearPMap
+
+variable {T : E →ₗ.[𝕜] F} [CompleteSpace E]
+
+theorem adjoint_isClosed (hT : Dense (T.domain : Set E)) :
+    T†.IsClosed := by
+  rw [IsClosed, adjoint_graph_eq_graph_adjoint hT, Submodule.adjoint]
+  simp only [Submodule.map_coe, WithLp.linearEquiv_apply]
+  rw [Equiv.image_eq_preimage]
+  exact (Submodule.isClosed_orthogonal _).preimage (WithLp.prod_continuous_equiv_symm _ _ _)
+
+/-- Every self-adjoint `LinearPMap` is closed. -/
+theorem _root_.IsSelfAdjoint.isClosed {A : E →ₗ.[𝕜] E} (hA : IsSelfAdjoint A) : A.IsClosed := by
+  rw [← isSelfAdjoint_def.mp hA]
+  exact adjoint_isClosed hA.dense_domain
+
+end LinearPMap

Following LinearAlgebra.Dual this makes NormedSpace.Dual reducible.

@@ -135,19 +135,10 @@ def adjointAux : T.adjointDomain →ₗ[𝕜] E where
     hT.eq_of_inner_left fun _ => by
       simp only [inner_add_left, Submodule.coe_add, InnerProductSpace.toDual_symm_apply,
         adjointDomainMkClmExtend_apply]
-      -- Porting note(https://github.com/leanprover-community/mathlib4/issues/5026):
-      -- mathlib3 was finished here
-      rw [adjointDomainMkClmExtend_apply, adjointDomainMkClmExtend_apply,
-        adjointDomainMkClmExtend_apply]
-      simp only [AddSubmonoid.coe_add, Submodule.coe_toAddSubmonoid, inner_add_left]
   map_smul' _ _ :=
     hT.eq_of_inner_left fun _ => by
       simp only [inner_smul_left, Submodule.coe_smul_of_tower, RingHom.id_apply,
         InnerProductSpace.toDual_symm_apply, adjointDomainMkClmExtend_apply]
-      -- Porting note(https://github.com/leanprover-community/mathlib4/issues/5026):
-      -- mathlib3 was finished here
-      rw [adjointDomainMkClmExtend_apply, adjointDomainMkClmExtend_apply]
-      simp only [Submodule.coe_smul_of_tower, inner_smul_left]
 #align linear_pmap.adjoint_aux LinearPMap.adjointAux
 
 theorem adjointAux_inner (y : T.adjointDomain) (x : T.domain) :

Also add a couple of refl and trans attributes

@@ -73,6 +73,7 @@ def IsFormalAdjoint (T : E →ₗ.[𝕜] F) (S : F →ₗ.[𝕜] E) : Prop :=
 
 variable {T : E →ₗ.[𝕜] F} {S : F →ₗ.[𝕜] E}
 
+@[symm]
 protected theorem IsFormalAdjoint.symm (h : T.IsFormalAdjoint S) :
     S.IsFormalAdjoint T := fun y _ => by
   rw [← inner_conj_symm, ← inner_conj_symm (y : F), h]

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -55,7 +55,7 @@ open IsROrC
 
 open scoped ComplexConjugate Classical
 
-variable {𝕜 E F G : Type _} [IsROrC 𝕜]
+variable {𝕜 E F G : Type*} [IsROrC 𝕜]
 
 variable [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
 

Define the star on LinearPMap as the adjoint and prove that every self-adjoint operator is automatically densely defined.

@@ -243,3 +243,36 @@ theorem toPMap_adjoint_eq_adjoint_toPMap_of_dense (hp : Dense (p : Set E)) :
 #align continuous_linear_map.to_pmap_adjoint_eq_adjoint_to_pmap_of_dense ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense
 
 end ContinuousLinearMap
+
+section Star
+
+namespace LinearPMap
+
+variable [CompleteSpace E]
+
+instance instStar : Star (E →ₗ.[𝕜] E) where
+  star := fun A ↦ A.adjoint
+
+variable {A : E →ₗ.[𝕜] E}
+
+theorem isSelfAdjoint_def : IsSelfAdjoint A ↔ A† = A := Iff.rfl
+
+/-- Every self-adjoint `LinearPMap` has dense domain.
+
+This is not true by definition since we define the adjoint without the assumption that the
+domain is dense, but the choice of the junk value implies that a `LinearPMap` cannot be self-adjoint
+if it does not have dense domain. -/
+theorem _root_.IsSelfAdjoint.dense_domain (hA : IsSelfAdjoint A) : Dense (A.domain : Set E) := by
+  by_contra h
+  rw [isSelfAdjoint_def] at hA
+  have h' : A.domain = ⊤ := by
+    rw [← hA, Submodule.eq_top_iff']
+    intro x
+    rw [mem_adjoint_domain_iff, ← hA]
+    refine (innerSL 𝕜 x).cont.comp ?_
+    simp [adjoint, h, continuous_const]
+  simp [h'] at h
+
+end LinearPMap
+
+end Star

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
-
-! This file was ported from Lean 3 source module analysis.inner_product_space.linear_pmap
-! leanprover-community/mathlib commit 8b981918a93bc45a8600de608cde7944a80d92b9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.InnerProductSpace.Adjoint
 import Mathlib.Topology.Algebra.Module.LinearPMap
 import Mathlib.Topology.Algebra.Module.Basic
 
+#align_import analysis.inner_product_space.linear_pmap from "leanprover-community/mathlib"@"8b981918a93bc45a8600de608cde7944a80d92b9"
+
 /-!
 
 # Partially defined linear operators on Hilbert spaces

Co-authored-by: Moritz Doll <moritz.doll@googlemail.com>