Theorems · Theorem · functional analysis
cfc_realPart
∀ {A : Type u_1} [inst : TopologicalSpace A] [inst_1 : Ring A] [inst_2 : StarRing A] [inst_3 : Algebra ℂ A]
[inst_4 : StarModule ℂ A] [inst_5 : ContinuousFunctionalCalculus ℂ A IsStarNormal] [ContinuousMap.UniqueHom ℂ A]
(f : ℂ → ℂ) (a : A),
autoParam (ContinuousOn f (spectrum ℂ ↑(realPart a))) cfc_realPart._auto_1 →
autoParam (IsStarNormal a) cfc_realPart._auto_3 → cfc f ↑(realPart a) = cfc (fun x => f ↑x.re) a- Cited by
- 0 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- RingHom.idstatement · cited by 18,349
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement · cited by 10,215
- Ringstatement and proof · cited by 7,463
- Complexstatement and proof · cited by 5,565
- AddSubgroupstatement · cited by 3,232
- StarRingstatement and proof · cited by 1,686
- Complex.ofRealstatement and proof · cited by 1,654
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