Theorems · Theorem · functional analysis

QuasispectrumRestricts.isSelfAdjoint

∀ {A : Type u_1} [inst : TopologicalSpace A] [inst_1 : NonUnitalRing A] [inst_2 : StarRing A] [inst_3 : Module ℂ A]
  [inst_4 : IsScalarTower ℂ A A] [inst_5 : SMulCommClass ℂ A A] [NonUnitalContinuousFunctionalCalculus ℂ A IsStarNormal]
  (a : A), QuasispectrumRestricts a ⇑Complex.reCLM → ∀ [IsStarNormal a], IsSelfAdjoint a

A normal element whose ℂ-quasispectrum is contained in ℝ is selfadjoint.

Defined in

Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances

Cited by

0 results in Mathlib

Foundations

Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceNonUnitalRingStarRingModuleIsScalarTowerSMulCommClassNonUnitalContinuousFunctionalCalculusIsStarNormal