Theorems · Theorem · functional analysis
cfc_real_eq_complex
∀ {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] {a : A} (f : ℝ → ℝ),
autoParam (IsSelfAdjoint a) cfc_real_eq_complex._auto_1 → cfc f a = cfc (fun x => ↑(f x.re)) a- Cited by
- 4 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.
Cites20
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
- Complexstatement and proof · cited by 5,565
- StarRingstatement and proof · cited by 1,686
- Complex.ofRealstatement · cited by 1,654
- T2Spacestatement and proof · cited by 1,351
- Complex.restatement · cited by 882
- IsSelfAdjointstatement and proof · cited by 545
- ContinuousFunctionalCalculusstatement and proof · cited by 331
- cfcstatement · cited by 228
Cited by4
Results whose statement or proof uses this declaration.
- cfc_complex_eq_realproof · cited by 0
- cfc_comp_reproof · cited by 0
- IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitaryproof · cited by 0
- cfc_comp_improof · cited by 0