Theorems · Theorem · functional analysis

norm_cfc_le

∀ {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] {f : 𝕜 → 𝕜}
  {a : A} {c : ℝ}, 0 ≤ c → (∀ x ∈ spectrum 𝕜 a, ‖f x‖ ≤ c) → ‖cfc f a‖ ≤ c

Defined in

Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric

Cited by

3 results in Mathlib

Foundations

Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedRingStarRingNormedAlgebraIsometricContinuousFunctionalCalculus