Theorems · Theorem · functional analysis
cfc_complex_eq_real
∀ {A : Type u_1} [inst : TopologicalSpace A] [inst_1 : Ring A] [inst_2 : StarRing A] [inst_3 : Algebra ℂ A]
[inst_4 : ContinuousFunctionalCalculus ℂ A IsStarNormal] [T2Space A] {f : ℂ → ℂ} (a : A),
(∀ x ∈ spectrum ℂ a, star (f x) = f x) →
autoParam (IsSelfAdjoint a) cfc_complex_eq_real._auto_1 → cfc f a = cfc (fun x => (f ↑x).re) a- Cited by
- 0 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- 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
- Complexstatement and proof · cited by 5,565
- StarRingstatement and proof · cited by 1,686
- Complex.ofRealstatement and proof · cited by 1,654
- T2Spacestatement and proof · cited by 1,351
- Star.starstatement and proof · cited by 1,082
- Complex.restatement and proof · cited by 882
- IsSelfAdjointstatement and proof · cited by 545
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.