Theorems · Theorem · functional analysis
Commute.cfc_real
∀ {A : Type u_2} [inst : Ring A] [inst_1 : StarRing A] [inst_2 : Algebra ℝ A] [inst_3 : TopologicalSpace A]
[inst_4 : ContinuousFunctionalCalculus ℝ A IsSelfAdjoint] [IsTopologicalRing A] [T2Space A] {a b : A},
Commute a b → ∀ (f : ℝ → ℝ), Commute (cfc f a) bA version of Commute.cfc or IsSelfAdjoint.commute_cfc which does not require any interaction
with star when the base ring is ℝ.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- StarRingstatement and proof · cited by 1,686
- ContinuousOnproof · cited by 1,411
- T2Spacestatement and proof · cited by 1,351
- Commutestatement and proof · cited by 639
- IsSelfAdjointstatement and proof · cited by 545
- spectrumproof · cited by 510
- IsTopologicalRingstatement and proof · cited by 402
- ContinuousFunctionalCalculusstatement and proof · cited by 331
Cited by1
Results whose statement or proof uses this declaration.
- Commute.cfc_nnrealproof · cited by 0