Theorems · Theorem · functional analysis
norm_cfcHom
∀ {𝕜 : Type u_1} {A : Type u_2} {p : outParam (A → Prop)} [inst : RCLike 𝕜] [inst_1 : NormedRing A]
[inst_2 : StarRing A] [inst_3 : NormedAlgebra 𝕜 A] [inst_4 : IsometricContinuousFunctionalCalculus 𝕜 A p] (a : A)
(f : C(↑(spectrum 𝕜 a), 𝕜)) (ha : autoParam (p a) norm_cfcHom._auto_1), ‖(cfcHom ⋯) f‖ = ‖f‖- Cited by
- 2 results in Mathlib
- Foundations
- Depth 178 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.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- Set.Elemstatement and proof · cited by 7,166
- Norm.normstatement · cited by 5,413
- RCLikestatement and proof · cited by 2,829
- ContinuousMapstatement and proof · cited by 2,491
- StarRingstatement and proof · cited by 1,686
- map_zeroproof · cited by 1,614
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- spectrumstatement and proof · cited by 510
Cited by2
Results whose statement or proof uses this declaration.
- IsGreatest.norm_cfcproof · cited by 6
- nnnorm_cfcHomproof · cited by 0