analysis.normed_space.algebra
⟷
Mathlib.Analysis.NormedSpace.Algebra
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.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -42,7 +42,7 @@ variable [NontriviallyNormedField 𝕜] [NormedRing A] [NormedAlgebra 𝕜 A] [C
#print WeakDual.CharacterSpace.norm_le_norm_one /-
theorem norm_le_norm_one (φ : characterSpace 𝕜 A) : ‖toNormedDual (φ : WeakDual 𝕜 A)‖ ≤ ‖(1 : A)‖ :=
- ContinuousLinearMap.op_norm_le_bound _ (norm_nonneg (1 : A)) fun a =>
+ ContinuousLinearMap.opNorm_le_bound _ (norm_nonneg (1 : A)) fun a =>
mul_comm ‖a‖ ‖(1 : A)‖ ▸ spectrum.norm_le_norm_mul_of_mem (apply_mem_spectrum φ a)
#align weak_dual.character_space.norm_le_norm_one WeakDual.CharacterSpace.norm_le_norm_one
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,9 +3,9 @@ Copyright (c) 2022 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
-import Mathbin.Topology.Algebra.Module.CharacterSpace
-import Mathbin.Analysis.NormedSpace.WeakDual
-import Mathbin.Analysis.NormedSpace.Spectrum
+import Topology.Algebra.Module.CharacterSpace
+import Analysis.NormedSpace.WeakDual
+import Analysis.NormedSpace.Spectrum
#align_import analysis.normed_space.algebra from "leanprover-community/mathlib"@"087c325ae0ab42dbdd5dee55bc37d3d5a0bf2197"
@@ -55,7 +55,7 @@ instance [ProperSpace 𝕜] : CompactSpace (characterSpace 𝕜 A) :=
intro φ hφ
rw [Set.mem_preimage, mem_closedBall_zero_iff]
exact (norm_le_norm_one ⟨φ, ⟨hφ.1, hφ.2⟩⟩ : _)
- exact isCompact_of_isClosed_subset (is_compact_closed_ball 𝕜 0 _) character_space.is_closed h
+ exact IsCompact.of_isClosed_subset (is_compact_closed_ball 𝕜 0 _) character_space.is_closed h
end CharacterSpace
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,16 +2,13 @@
Copyright (c) 2022 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-
-! This file was ported from Lean 3 source module analysis.normed_space.algebra
-! leanprover-community/mathlib commit 087c325ae0ab42dbdd5dee55bc37d3d5a0bf2197
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Topology.Algebra.Module.CharacterSpace
import Mathbin.Analysis.NormedSpace.WeakDual
import Mathbin.Analysis.NormedSpace.Spectrum
+#align_import analysis.normed_space.algebra from "leanprover-community/mathlib"@"087c325ae0ab42dbdd5dee55bc37d3d5a0bf2197"
+
/-!
# Normed algebras
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -43,10 +43,12 @@ namespace CharacterSpace
variable [NontriviallyNormedField 𝕜] [NormedRing A] [NormedAlgebra 𝕜 A] [CompleteSpace A]
+#print WeakDual.CharacterSpace.norm_le_norm_one /-
theorem norm_le_norm_one (φ : characterSpace 𝕜 A) : ‖toNormedDual (φ : WeakDual 𝕜 A)‖ ≤ ‖(1 : A)‖ :=
ContinuousLinearMap.op_norm_le_bound _ (norm_nonneg (1 : A)) fun a =>
mul_comm ‖a‖ ‖(1 : A)‖ ▸ spectrum.norm_le_norm_mul_of_mem (apply_mem_spectrum φ a)
#align weak_dual.character_space.norm_le_norm_one WeakDual.CharacterSpace.norm_le_norm_one
+-/
instance [ProperSpace 𝕜] : CompactSpace (characterSpace 𝕜 A) :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
! This file was ported from Lean 3 source module analysis.normed_space.algebra
-! leanprover-community/mathlib commit 17ef379e997badd73e5eabb4d38f11919ab3c4b3
+! leanprover-community/mathlib commit 087c325ae0ab42dbdd5dee55bc37d3d5a0bf2197
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -15,6 +15,9 @@ import Mathbin.Analysis.NormedSpace.Spectrum
/-!
# Normed algebras
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
This file contains basic facts about normed algebras.
## Main results
mathlib commit https://github.com/leanprover-community/mathlib/commit/c471da714c044131b90c133701e51b877c246677
@@ -43,7 +43,7 @@ variable [NontriviallyNormedField 𝕜] [NormedRing A] [NormedAlgebra 𝕜 A] [C
theorem norm_le_norm_one (φ : characterSpace 𝕜 A) : ‖toNormedDual (φ : WeakDual 𝕜 A)‖ ≤ ‖(1 : A)‖ :=
ContinuousLinearMap.op_norm_le_bound _ (norm_nonneg (1 : A)) fun a =>
mul_comm ‖a‖ ‖(1 : A)‖ ▸ spectrum.norm_le_norm_mul_of_mem (apply_mem_spectrum φ a)
-#align weak_dual.character_space.norm_le_norm_one WeakDual.characterSpace.norm_le_norm_one
+#align weak_dual.character_space.norm_le_norm_one WeakDual.CharacterSpace.norm_le_norm_one
instance [ProperSpace 𝕜] : CompactSpace (characterSpace 𝕜 A) :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -38,7 +38,7 @@ namespace CharacterSpace
variable [NontriviallyNormedField 𝕜] [NormedRing A] [NormedAlgebra 𝕜 A] [CompleteSpace A]
theorem norm_le_norm_one (φ : characterSpace 𝕜 A) : ‖toNormedDual (φ : WeakDual 𝕜 A)‖ ≤ ‖(1 : A)‖ :=
- ContinuousLinearMap.op_norm_le_bound _ (norm_nonneg (1 : A)) fun a =>
+ ContinuousLinearMap.opNorm_le_bound _ (norm_nonneg (1 : A)) fun a =>
mul_comm ‖a‖ ‖(1 : A)‖ ▸ spectrum.norm_le_norm_mul_of_mem (apply_mem_spectrum φ a)
#align weak_dual.character_space.norm_le_norm_one WeakDual.CharacterSpace.norm_le_norm_one
@@ -48,7 +48,7 @@ instance [ProperSpace 𝕜] : CompactSpace (characterSpace 𝕜 A) := by
intro φ hφ
rw [Set.mem_preimage, mem_closedBall_zero_iff]
exact (norm_le_norm_one ⟨φ, ⟨hφ.1, hφ.2⟩⟩ : _)
- exact isCompact_of_isClosed_subset (isCompact_closedBall 𝕜 0 _) CharacterSpace.isClosed h
+ exact (isCompact_closedBall 𝕜 0 _).of_isClosed_subset CharacterSpace.isClosed h
end CharacterSpace
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -29,7 +29,7 @@ normed algebra, character space, continuous functional calculus
-/
-variable {𝕜 : Type _} {A : Type _}
+variable {𝕜 : Type*} {A : Type*}
namespace WeakDual
@@ -2,16 +2,13 @@
Copyright (c) 2022 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-
-! This file was ported from Lean 3 source module analysis.normed_space.algebra
-! leanprover-community/mathlib commit 17ef379e997badd73e5eabb4d38f11919ab3c4b3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Topology.Algebra.Module.CharacterSpace
import Mathlib.Analysis.NormedSpace.WeakDual
import Mathlib.Analysis.NormedSpace.Spectrum
+#align_import analysis.normed_space.algebra from "leanprover-community/mathlib"@"17ef379e997badd73e5eabb4d38f11919ab3c4b3"
+
/-!
# Normed algebras
The unported dependencies are
algebra.order.module
init.core
linear_algebra.free_module.finite.rank
algebra.order.monoid.cancel.defs
algebra.abs
algebra.group_power.lemmas
init.data.list.basic
linear_algebra.free_module.rank
algebra.order.monoid.cancel.basic
init.data.list.default
topology.subset_properties
init.logic
The following 1 dependencies have changed in mathlib3 since they were ported, which may complicate porting this file