Theorems · Theorem · functional analysis
IsSelfAdjoint.commute_cfcHom
∀ {𝕜 : Type u_1} {A : Type u_2} {p : A → Prop} [inst : RCLike 𝕜] [inst_1 : Ring A] [inst_2 : StarRing A]
[inst_3 : Algebra 𝕜 A] [inst_4 : TopologicalSpace A] [inst_5 : ContinuousFunctionalCalculus 𝕜 A p]
[IsSemitopologicalRing A] [T2Space A] {a b : A} (ha : p a),
IsSelfAdjoint a → Commute a b → ∀ (f : C(↑(spectrum 𝕜 a), 𝕜)), Commute ((cfcHom ha) f) b- Cited by
- 0 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Set.Elemstatement and proof · cited by 7,166
- RCLikestatement and proof · cited by 2,829
- ContinuousMapstatement and proof · cited by 2,491
- StarRingstatement and proof · cited by 1,686
- T2Spacestatement and proof · cited by 1,351
- Commutestatement and proof · cited by 639
- IsSelfAdjointstatement and proof · cited by 545
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