analysis.von_neumann_algebra.basic | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

46b633fd

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

af471b9e

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,11 +3,11 @@ Copyright (c) 2022 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathbin.Analysis.NormedSpace.Dual
-import Mathbin.Analysis.NormedSpace.Star.Basic
-import Mathbin.Analysis.Complex.Basic
-import Mathbin.Analysis.InnerProductSpace.Adjoint
-import Mathbin.Algebra.Star.Subalgebra
+import Analysis.NormedSpace.Dual
+import Analysis.NormedSpace.Star.Basic
+import Analysis.Complex.Basic
+import Analysis.InnerProductSpace.Adjoint
+import Algebra.Star.Subalgebra
 
 #align_import analysis.von_neumann_algebra.basic from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"

af471b9e

bump to nightly-2023-08-17-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

60285dcc

Diff

@@ -96,7 +96,7 @@ instance : StarMemClass (VonNeumannAlgebra H) (H →L[ℂ] H) where star_mem s a
 instance : SubringClass (VonNeumannAlgebra H) (H →L[ℂ] H)
     where
   add_mem := add_mem'
-  mul_mem := mul_mem'
+  hMul_mem := hMul_mem'
   one_mem := one_mem'
   zero_mem := zero_mem'
   neg_mem s a ha := show -a ∈ s.toStarSubalgebra from neg_mem ha

af471b9e

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module analysis.von_neumann_algebra.basic
-! leanprover-community/mathlib commit af471b9e3ce868f296626d33189b4ce730fa4c00
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.NormedSpace.Dual
 import Mathbin.Analysis.NormedSpace.Star.Basic
@@ -14,6 +9,8 @@ import Mathbin.Analysis.Complex.Basic
 import Mathbin.Analysis.InnerProductSpace.Adjoint
 import Mathbin.Algebra.Star.Subalgebra
 
+#align_import analysis.von_neumann_algebra.basic from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
+
 /-!
 # Von Neumann algebras

af471b9e

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -36,6 +36,7 @@ that the concrete definition is equivalent to a *-closed subalgebra which is wea
 
 universe u v
 
+#print WStarAlgebra /-
 /-- Sakai's definition of a von Neumann algebra as a C^* algebra with a Banach space predual.
 
 So that we can unambiguously talk about these "abstract" von Neumann algebras
@@ -55,7 +56,9 @@ class WStarAlgebra (M : Type u) [NormedRing M] [StarRing M] [CstarRing M] [Modul
     ∃ (X : Type u) (_ : NormedAddCommGroup X) (_ : NormedSpace ℂ X) (_ : CompleteSpace X),
       Nonempty (NormedSpace.Dual ℂ X ≃ₗᵢ⋆[ℂ] M)
 #align wstar_algebra WStarAlgebra
+-/
 
+#print VonNeumannAlgebra /-
 -- TODO: Without this, `von_neumann_algebra` times out. Why?
 /-- The double commutant definition of a von Neumann algebra,
 as a *-closed subalgebra of bounded operators on a Hilbert space,
@@ -76,6 +79,7 @@ structure VonNeumannAlgebra (H : Type u) [NormedAddCommGroup H] [InnerProductSpa
     [CompleteSpace H] extends StarSubalgebra ℂ (H →L[ℂ] H) where
   centralizer_centralizer' : Set.centralizer (Set.centralizer carrier) = carrier
 #align von_neumann_algebra VonNeumannAlgebra
+-/
 
 /-- Consider a von Neumann algebra acting on a Hilbert space `H` as a *-subalgebra of `H →L[ℂ] H`.
 (That is, we forget that it is equal to its double commutant
@@ -106,17 +110,22 @@ theorem mem_carrier {S : VonNeumannAlgebra H} {x : H →L[ℂ] H} :
   Iff.rfl
 #align von_neumann_algebra.mem_carrier VonNeumannAlgebra.mem_carrierₓ
 
+#print VonNeumannAlgebra.ext /-
 @[ext]
 theorem ext {S T : VonNeumannAlgebra H} (h : ∀ x, x ∈ S ↔ x ∈ T) : S = T :=
   SetLike.ext h
 #align von_neumann_algebra.ext VonNeumannAlgebra.ext
+-/
 
+#print VonNeumannAlgebra.centralizer_centralizer /-
 @[simp]
 theorem centralizer_centralizer (S : VonNeumannAlgebra H) :
     Set.centralizer (Set.centralizer (S : Set (H →L[ℂ] H))) = S :=
   S.centralizer_centralizer'
 #align von_neumann_algebra.centralizer_centralizer VonNeumannAlgebra.centralizer_centralizer
+-/
 
+#print VonNeumannAlgebra.commutant /-
 /-- The centralizer of a `von_neumann_algebra`, as a `von_neumann_algebra`.-/
 def commutant (S : VonNeumannAlgebra H) : VonNeumannAlgebra H :=
   {
@@ -125,23 +134,30 @@ def commutant (S : VonNeumannAlgebra H) : VonNeumannAlgebra H :=
     carrier := Set.centralizer (S : Set (H →L[ℂ] H))
     centralizer_centralizer' := by rw [S.centralizer_centralizer] }
 #align von_neumann_algebra.commutant VonNeumannAlgebra.commutant
+-/
 
+#print VonNeumannAlgebra.coe_commutant /-
 @[simp]
 theorem coe_commutant (S : VonNeumannAlgebra H) :
     ↑S.commutant = Set.centralizer (S : Set (H →L[ℂ] H)) :=
   rfl
 #align von_neumann_algebra.coe_commutant VonNeumannAlgebra.coe_commutant
+-/
 
+#print VonNeumannAlgebra.mem_commutant_iff /-
 @[simp]
 theorem mem_commutant_iff {S : VonNeumannAlgebra H} {z : H →L[ℂ] H} :
     z ∈ S.commutant ↔ ∀ g ∈ S, g * z = z * g :=
   Iff.rfl
 #align von_neumann_algebra.mem_commutant_iff VonNeumannAlgebra.mem_commutant_iff
+-/
 
+#print VonNeumannAlgebra.commutant_commutant /-
 @[simp]
 theorem commutant_commutant (S : VonNeumannAlgebra H) : S.commutant.commutant = S :=
   SetLike.coe_injective S.centralizer_centralizer'
 #align von_neumann_algebra.commutant_commutant VonNeumannAlgebra.commutant_commutant
+-/
 
 end VonNeumannAlgebra

af471b9e

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module analysis.von_neumann_algebra.basic
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
+! leanprover-community/mathlib commit af471b9e3ce868f296626d33189b4ce730fa4c00
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.Algebra.Star.Subalgebra
 /-!
 # Von Neumann algebras
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We give the "abstract" and "concrete" definitions of a von Neumann algebra.
 We still have a major project ahead of us to show the equivalence between these definitions!
 
@@ -46,12 +49,12 @@ One the other hand, not picking one means that the weak-* topology
 (which depends on a choice of predual) must be defined using the choice,
 and we may be unhappy with the resulting opaqueness of the definition.
 -/
-class WstarAlgebra (M : Type u) [NormedRing M] [StarRing M] [CstarRing M] [Module ℂ M]
+class WStarAlgebra (M : Type u) [NormedRing M] [StarRing M] [CstarRing M] [Module ℂ M]
     [NormedAlgebra ℂ M] [StarModule ℂ M] where
   exists_predual :
     ∃ (X : Type u) (_ : NormedAddCommGroup X) (_ : NormedSpace ℂ X) (_ : CompleteSpace X),
       Nonempty (NormedSpace.Dual ℂ X ≃ₗᵢ⋆[ℂ] M)
-#align wstar_algebra WstarAlgebra
+#align wstar_algebra WStarAlgebra
 
 -- TODO: Without this, `von_neumann_algebra` times out. Why?
 /-- The double commutant definition of a von Neumann algebra,
@@ -101,7 +104,7 @@ instance : SubringClass (VonNeumannAlgebra H) (H →L[ℂ] H)
 theorem mem_carrier {S : VonNeumannAlgebra H} {x : H →L[ℂ] H} :
     x ∈ S.carrier ↔ x ∈ (S : Set (H →L[ℂ] H)) :=
   Iff.rfl
-#align von_neumann_algebra.mem_carrier VonNeumannAlgebra.mem_carrier
+#align von_neumann_algebra.mem_carrier VonNeumannAlgebra.mem_carrierₓ
 
 @[ext]
 theorem ext {S T : VonNeumannAlgebra H} (h : ∀ x, x ∈ S ↔ x ∈ T) : S = T :=

46b633fd

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -47,9 +47,9 @@ One the other hand, not picking one means that the weak-* topology
 and we may be unhappy with the resulting opaqueness of the definition.
 -/
 class WstarAlgebra (M : Type u) [NormedRing M] [StarRing M] [CstarRing M] [Module ℂ M]
-  [NormedAlgebra ℂ M] [StarModule ℂ M] where
+    [NormedAlgebra ℂ M] [StarModule ℂ M] where
   exists_predual :
-    ∃ (X : Type u)(_ : NormedAddCommGroup X)(_ : NormedSpace ℂ X)(_ : CompleteSpace X),
+    ∃ (X : Type u) (_ : NormedAddCommGroup X) (_ : NormedSpace ℂ X) (_ : CompleteSpace X),
       Nonempty (NormedSpace.Dual ℂ X ≃ₗᵢ⋆[ℂ] M)
 #align wstar_algebra WstarAlgebra
 
@@ -70,7 +70,7 @@ and instead will use `⊤ : von_neumann_algebra H`.
 -/
 @[nolint has_nonempty_instance]
 structure VonNeumannAlgebra (H : Type u) [NormedAddCommGroup H] [InnerProductSpace ℂ H]
-  [CompleteSpace H] extends StarSubalgebra ℂ (H →L[ℂ] H) where
+    [CompleteSpace H] extends StarSubalgebra ℂ (H →L[ℂ] H) where
   centralizer_centralizer' : Set.centralizer (Set.centralizer carrier) = carrier
 #align von_neumann_algebra VonNeumannAlgebra
 
@@ -85,7 +85,7 @@ namespace VonNeumannAlgebra
 variable {H : Type u} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H]
 
 instance : SetLike (VonNeumannAlgebra H) (H →L[ℂ] H) :=
-  ⟨VonNeumannAlgebra.carrier, fun S T h => by cases S <;> cases T <;> congr ⟩
+  ⟨VonNeumannAlgebra.carrier, fun S T h => by cases S <;> cases T <;> congr⟩
 
 instance : StarMemClass (VonNeumannAlgebra H) (H →L[ℂ] H) where star_mem s a := s.star_mem'

46b633fd

bump to nightly-2023-03-26-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/55d771df074d0dd020139ee1cd4b95521422df9f

ca5de00c

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module analysis.von_neumann_algebra.basic
-! leanprover-community/mathlib commit 160ef3e338a2a4f21a280e4c152d4016156e516d
+! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -69,8 +69,8 @@ Thus we can't say that the bounded operators `H →L[ℂ] H` form a `von_neumann
 and instead will use `⊤ : von_neumann_algebra H`.
 -/
 @[nolint has_nonempty_instance]
-structure VonNeumannAlgebra (H : Type u) [InnerProductSpace ℂ H] [CompleteSpace H] extends
-  StarSubalgebra ℂ (H →L[ℂ] H) where
+structure VonNeumannAlgebra (H : Type u) [NormedAddCommGroup H] [InnerProductSpace ℂ H]
+  [CompleteSpace H] extends StarSubalgebra ℂ (H →L[ℂ] H) where
   centralizer_centralizer' : Set.centralizer (Set.centralizer carrier) = carrier
 #align von_neumann_algebra VonNeumannAlgebra
 
@@ -82,7 +82,7 @@ add_decl_doc VonNeumannAlgebra.toStarSubalgebra
 
 namespace VonNeumannAlgebra
 
-variable {H : Type u} [InnerProductSpace ℂ H] [CompleteSpace H]
+variable {H : Type u} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H]
 
 instance : SetLike (VonNeumannAlgebra H) (H →L[ℂ] H) :=
   ⟨VonNeumannAlgebra.carrier, fun S T h => by cases S <;> cases T <;> congr ⟩

160ef3e3

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

46b633fd

style: replace '.-/' by '. -/' (#11938)

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

3556ded2

Diff

@@ -127,7 +127,7 @@ theorem centralizer_centralizer (S : VonNeumannAlgebra H) :
   S.centralizer_centralizer'
 #align von_neumann_algebra.centralizer_centralizer VonNeumannAlgebra.centralizer_centralizer
 
-/-- The centralizer of a `VonNeumannAlgebra`, as a `VonNeumannAlgebra`.-/
+/-- The centralizer of a `VonNeumannAlgebra`, as a `VonNeumannAlgebra`. -/
 def commutant (S : VonNeumannAlgebra H) : VonNeumannAlgebra H where
   toStarSubalgebra := StarSubalgebra.centralizer ℂ (S : Set (H →L[ℂ] H))
   centralizer_centralizer' := by simp

46b633fd

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

converts "--porting note" into "-- Porting note";
converts "porting note" into "Porting note".

8be0b69c

Diff

@@ -67,7 +67,7 @@ Thus we can't say that the bounded operators `H →L[ℂ] H` form a `VonNeumannA
 (although we will later construct the instance `WStarAlgebra (H →L[ℂ] H)`),
 and instead will use `⊤ : VonNeumannAlgebra H`.
 -/
--- porting note: I don't think the nonempty instance linter exists yet
+-- Porting note: I don't think the nonempty instance linter exists yet
 structure VonNeumannAlgebra (H : Type u) [NormedAddCommGroup H] [InnerProductSpace ℂ H]
     [CompleteSpace H] extends StarSubalgebra ℂ (H →L[ℂ] H) where
   /-- The double commutant (a.k.a. centralizer) of a `VonNeumannAlgebra` is itself. -/
@@ -88,7 +88,7 @@ instance instSetLike : SetLike (VonNeumannAlgebra H) (H →L[ℂ] H) where
   coe S := S.carrier
   coe_injective' S T h := by obtain ⟨⟨⟨⟨⟨⟨_, _⟩, _⟩, _⟩, _⟩, _⟩, _⟩ := S; cases T; congr
 
--- porting note: `StarMemClass` should be in `Prop`?
+-- Porting note: `StarMemClass` should be in `Prop`?
 noncomputable instance instStarMemClass : StarMemClass (VonNeumannAlgebra H) (H →L[ℂ] H) where
   star_mem {s} := s.star_mem'
 
@@ -104,7 +104,7 @@ theorem mem_carrier {S : VonNeumannAlgebra H} {x : H →L[ℂ] H} :
     x ∈ S.toStarSubalgebra ↔ x ∈ (S : Set (H →L[ℂ] H)) :=
   Iff.rfl
 #align von_neumann_algebra.mem_carrier VonNeumannAlgebra.mem_carrierₓ
--- porting note: changed the declaration because `simpNF` indicated the LHS simplifies to this.
+-- Porting note: changed the declaration because `simpNF` indicated the LHS simplifies to this.
 
 @[simp]
 theorem coe_toStarSubalgebra (S : VonNeumannAlgebra H) :

46b633fd

chore: space after ← (#8178)

Co-authored-by: Moritz Firsching <firsching@google.com>

5fb9beab

Diff

@@ -143,7 +143,7 @@ theorem coe_commutant (S : VonNeumannAlgebra H) :
 @[simp]
 theorem mem_commutant_iff {S : VonNeumannAlgebra H} {z : H →L[ℂ] H} :
     z ∈ S.commutant ↔ ∀ g ∈ S, g * z = z * g := by
-  rw [←SetLike.mem_coe, coe_commutant]
+  rw [← SetLike.mem_coe, coe_commutant]
   rfl
 #align von_neumann_algebra.mem_commutant_iff VonNeumannAlgebra.mem_commutant_iff

46b633fd

feat: Linter that checks that Prop classes are Props (#6148)

930dd29d

Diff

@@ -44,7 +44,7 @@ One the other hand, not picking one means that the weak-* topology
 and we may be unhappy with the resulting opaqueness of the definition.
 -/
 class WStarAlgebra (M : Type u) [NormedRing M] [StarRing M] [CstarRing M] [Module ℂ M]
-    [NormedAlgebra ℂ M] [StarModule ℂ M] where
+    [NormedAlgebra ℂ M] [StarModule ℂ M] : Prop where
   /-- There is a Banach space `X` whose dual is isometrically (conjugate-linearly) isomorphic
   to the `WStarAlgebra`. -/
   exists_predual :

46b633fd

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module analysis.von_neumann_algebra.basic
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.NormedSpace.Dual
 import Mathlib.Analysis.NormedSpace.Star.Basic
@@ -14,6 +9,8 @@ import Mathlib.Analysis.Complex.Basic
 import Mathlib.Analysis.InnerProductSpace.Adjoint
 import Mathlib.Algebra.Star.Subalgebra
 
+#align_import analysis.von_neumann_algebra.basic from "leanprover-community/mathlib"@"46b633fd842bef9469441c0209906f6dddd2b4f5"
+
 /-!
 # Von Neumann algebras

46b633fd

feat: define NonUnitalStarSubalgebras and develop basic API (#5537)

This continues the non-unital-ization of mathlib

This PR also redefines StarSubalgebra.centralizer so that it no longer requires the set s provided to be closed under star, and instead the carrier is just the Set.centralizer (s ∪ star s). Consequently, this changes some things in von Neumann algebras, where we now need to see that Set.centralizer (↑S ∪ star ↑S) = Set.centralizer ↑S, where S is a StarSubalgebra. Therefore we add the simp lemma StarMemClass.star_coe_eq.

depends on: #5151
depends on: #5512

15ef30fa

Diff

@@ -109,6 +109,16 @@ theorem mem_carrier {S : VonNeumannAlgebra H} {x : H →L[ℂ] H} :
 #align von_neumann_algebra.mem_carrier VonNeumannAlgebra.mem_carrierₓ
 -- porting note: changed the declaration because `simpNF` indicated the LHS simplifies to this.
 
+@[simp]
+theorem coe_toStarSubalgebra (S : VonNeumannAlgebra H) :
+    (S.toStarSubalgebra : Set (H →L[ℂ] H)) = S :=
+  rfl
+
+@[simp]
+theorem coe_mk (S : StarSubalgebra ℂ (H →L[ℂ] H)) (h) :
+    ((⟨S, h⟩ : VonNeumannAlgebra H) : Set (H →L[ℂ] H)) = S :=
+  rfl
+
 @[ext]
 theorem ext {S T : VonNeumannAlgebra H} (h : ∀ x, x ∈ S ↔ x ∈ T) : S = T :=
   SetLike.ext h
@@ -121,29 +131,28 @@ theorem centralizer_centralizer (S : VonNeumannAlgebra H) :
 #align von_neumann_algebra.centralizer_centralizer VonNeumannAlgebra.centralizer_centralizer
 
 /-- The centralizer of a `VonNeumannAlgebra`, as a `VonNeumannAlgebra`.-/
-def commutant (S : VonNeumannAlgebra H) : VonNeumannAlgebra H :=
-  {
-    StarSubalgebra.centralizer ℂ (S : Set (H →L[ℂ] H)) fun a (ha : a ∈ S) =>
-      (star_mem ha : _) with
-    carrier := Set.centralizer (S : Set (H →L[ℂ] H))
-    centralizer_centralizer' := by rw [S.centralizer_centralizer] }
+def commutant (S : VonNeumannAlgebra H) : VonNeumannAlgebra H where
+  toStarSubalgebra := StarSubalgebra.centralizer ℂ (S : Set (H →L[ℂ] H))
+  centralizer_centralizer' := by simp
 #align von_neumann_algebra.commutant VonNeumannAlgebra.commutant
 
 @[simp]
 theorem coe_commutant (S : VonNeumannAlgebra H) :
-    ↑S.commutant = Set.centralizer (S : Set (H →L[ℂ] H)) :=
-  rfl
+    ↑S.commutant = Set.centralizer (S : Set (H →L[ℂ] H)) := by
+  simp [commutant]
+
 #align von_neumann_algebra.coe_commutant VonNeumannAlgebra.coe_commutant
 
 @[simp]
 theorem mem_commutant_iff {S : VonNeumannAlgebra H} {z : H →L[ℂ] H} :
-    z ∈ S.commutant ↔ ∀ g ∈ S, g * z = z * g :=
-  Iff.rfl
+    z ∈ S.commutant ↔ ∀ g ∈ S, g * z = z * g := by
+  rw [←SetLike.mem_coe, coe_commutant]
+  rfl
 #align von_neumann_algebra.mem_commutant_iff VonNeumannAlgebra.mem_commutant_iff
 
 @[simp]
 theorem commutant_commutant (S : VonNeumannAlgebra H) : S.commutant.commutant = S :=
-  SetLike.coe_injective S.centralizer_centralizer'
+  SetLike.coe_injective <| by simp
 #align von_neumann_algebra.commutant_commutant VonNeumannAlgebra.commutant_commutant
 
 end VonNeumannAlgebra

46b633fd

chore: fix many typos (#4967)

These are all doc fixes

6f9e51c3

Diff

@@ -70,7 +70,7 @@ Thus we can't say that the bounded operators `H →L[ℂ] H` form a `VonNeumannA
 (although we will later construct the instance `WStarAlgebra (H →L[ℂ] H)`),
 and instead will use `⊤ : VonNeumannAlgebra H`.
 -/
--- porting note: I don't think the nonempty intance linter exists yet
+-- porting note: I don't think the nonempty instance linter exists yet
 structure VonNeumannAlgebra (H : Type u) [NormedAddCommGroup H] [InnerProductSpace ℂ H]
     [CompleteSpace H] extends StarSubalgebra ℂ (H →L[ℂ] H) where
   /-- The double commutant (a.k.a. centralizer) of a `VonNeumannAlgebra` is itself. -/

46b633fd

feat: port Analysis.VonNeumannAlgebra.Basic (#4569)

488dc767

`analysis.von_neumann_algebra.basic` ⟷ `Mathlib.Analysis.VonNeumannAlgebra.Basic`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 917

analysis.von_neumann_algebra.basic ⟷ Mathlib.Analysis.VonNeumannAlgebra.Basic

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 917

`analysis.von_neumann_algebra.basic` ⟷ `Mathlib.Analysis.VonNeumannAlgebra.Basic`