Theorems · Theorem · functional analysis

Commute.cfcAbs_mul_eq

∀ {A : Type u_2} [inst : NonUnitalRing A] [inst_1 : StarRing A] [inst_2 : TopologicalSpace A] [inst_3 : Module ℝ A]
  [inst_4 : SMulCommClass ℝ A A] [inst_5 : IsScalarTower ℝ A A]
  [inst_6 : NonUnitalContinuousFunctionalCalculus ℝ A IsSelfAdjoint] [inst_7 : PartialOrder A]
  [inst_8 : StarOrderedRing A] [inst_9 : NonnegSpectrumClass ℝ A] [IsTopologicalRing A] [T2Space A] {a b : A},
  Commute a b → Commute a (star b) → CFC.abs (a * b) = CFC.abs a * CFC.abs b

Defined in

Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs

Cited by

1 results in Mathlib

Foundations

Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonUnitalRingStarRingTopologicalSpaceModuleSMulCommClassIsScalarTowerNonUnitalContinuousFunctionalCalculusPartialOrderStarOrderedRingNonnegSpectrumClassIsTopologicalRingT2Space