Theorems · Theorem · functional analysis
Commute.cfc_nnreal
∀ {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] [inst_7 : PartialOrder A]
[inst_8 : NonnegSpectrumClass ℝ A] [inst_9 : StarOrderedRing A] {a b : A},
Commute a b → ∀ (f : NNReal → NNReal), 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≥0.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites24
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
- CommSemiringproof · cited by 10,911
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- NNRealstatement and proof · cited by 4,310
- StarRingstatement and proof · cited by 1,686
- MetricSpaceproof · cited by 1,684
- T2Spacestatement and proof · cited by 1,351
- NNReal.toRealproof · cited by 1,260
- Commutestatement and proof · cited by 639
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