Theorems · Theorem · functional analysis
NonUnitalStarAlgHom.norm_apply_le
∀ {F : Type u_1} {A : Type u_2} {B : Type u_3} [inst : NonUnitalCStarAlgebra A] [inst_1 : NonUnitalCStarAlgebra B]
[inst_2 : FunLike F A B] [NonUnitalAlgHomClass F ℂ A B] [StarHomClass F A B] (φ : F) (a : A), ‖φ a‖ ≤ ‖a‖A non-unital star algebra homomorphism of complex C⋆-algebras is norm contractive.
- Defined in
- Mathlib.Analysis.CStarAlgebra.Spectrum
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 289 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- Realstatement · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- FunLikestatement and proof · cited by 2,560
- NonUnitalCStarAlgebrastatement and proof · cited by 149
- StarHomClassstatement and proof · cited by 76
- NonUnitalAlgHomClassstatement and proof · cited by 75
- NonUnitalStarAlgHom.nnnorm_apply_leproof · cited by 2
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