Theorems · Theorem · functional analysis

NonUnitalStarAlgHom.nnnorm_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

2 results in Mathlib

Foundations

Depth 288 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonUnitalCStarAlgebraNonUnitalCStarAlgebraFunLikeNonUnitalAlgHomClassStarHomClass