Theorems · Theorem · functional analysis

CFC.quasispectrum_zero_eq

∀ {R : Type u_1} {A : Type u_2} {p : A → Prop} [inst : CommSemiring R] [inst_1 : Nontrivial R] [inst_2 : StarRing R]
  [inst_3 : MetricSpace R] [inst_4 : IsTopologicalSemiring R] [inst_5 : ContinuousStar R] [inst_6 : NonUnitalRing A]
  [inst_7 : StarRing A] [inst_8 : TopologicalSpace A] [inst_9 : Module R A] [inst_10 : IsScalarTower R A A]
  [inst_11 : SMulCommClass R A A] [instCFCₙ : NonUnitalContinuousFunctionalCalculus R A p], quasispectrum R 0 = {0}

Defined in

Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital

Cited by

1 results in Mathlib

Foundations

Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringNontrivialStarRingMetricSpaceIsTopologicalSemiringContinuousStarNonUnitalRingStarRingTopologicalSpaceModuleIsScalarTowerSMulCommClassNonUnitalContinuousFunctionalCalculus