Theorems · Theorem · functional analysis

NonUnitalIsometricContinuousFunctionalCalculus.nnnorm_quasispectrum_le

∀ {𝕜 : Type u_1} {A : Type u_2} {p : outParam (A → Prop)} [inst : RCLike 𝕜] [inst_1 : NonUnitalNormedRing A]
  [inst_2 : StarRing A] [inst_3 : NormedSpace 𝕜 A] [inst_4 : IsScalarTower 𝕜 A A] [inst_5 : SMulCommClass 𝕜 A A]
  [NonUnitalIsometricContinuousFunctionalCalculus 𝕜 A p] (a : A) ⦃x : 𝕜⦄,
  x ∈ quasispectrum 𝕜 a →
    autoParam (p a) NonUnitalIsometricContinuousFunctionalCalculus.nnnorm_quasispectrum_le._auto_1 → ‖x‖₊ ≤ ‖a‖₊

Defined in

Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric

Cited by

0 results in Mathlib

Foundations

Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNonUnitalNormedRingStarRingNormedSpaceIsScalarTowerSMulCommClassNonUnitalIsometricContinuousFunctionalCalculus