Theorems · Theorem · functional analysis

quasispectrum_realPart

∀ {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] [inst_6 : StarModule ℂ A]
  [NonUnitalContinuousFunctionalCalculus ℂ A IsStarNormal] (a : A),
  autoParam (IsStarNormal a) quasispectrum_realPart._auto_1 →
    quasispectrum ℂ ↑(realPart a) = (fun x => ↑x.re) '' quasispectrum ℂ a

Defined in

Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.RealImaginaryPart

Cited by

2 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceNonUnitalRingStarRingModuleIsScalarTowerSMulCommClassStarModuleNonUnitalContinuousFunctionalCalculus