Theorems · Theorem · functional analysis

CFC.continuousOn_rpow

∀ {A : Type u_1} [inst : NormedRing A] [inst_1 : StarRing A] [inst_2 : NormedAlgebra ℝ A] [inst_3 : PartialOrder A]
  [inst_4 : StarOrderedRing A] [inst_5 : NonnegSpectrumClass ℝ A]
  [inst_6 : IsometricContinuousFunctionalCalculus ℝ A IsSelfAdjoint] [ContinuousStar A] [CompleteSpace A] (r : ℝ),
  ContinuousOn (fun x => x ^ r) {a | IsStrictlyPositive a}

Defined in

Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Isometric

Cited by

0 results in Mathlib

Foundations

Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedRingStarRingNormedAlgebraPartialOrderStarOrderedRingNonnegSpectrumClassIsometricContinuousFunctionalCalculusContinuousStarCompleteSpace