Theorems · Theorem · functional analysis

CFC.continuousOn_sqrt

∀ {A : Type u_1} [inst : NonUnitalNormedRing A] [inst_1 : StarRing A] [inst_2 : NormedSpace ℝ A]
  [inst_3 : IsScalarTower ℝ A A] [inst_4 : SMulCommClass ℝ A A] [inst_5 : PartialOrder A] [inst_6 : StarOrderedRing A]
  [inst_7 : NonnegSpectrumClass ℝ A] [inst_8 : NonUnitalIsometricContinuousFunctionalCalculus ℝ A IsSelfAdjoint]
  [ContinuousStar A] [CompleteSpace A], ContinuousOn CFC.sqrt {a | 0 ≤ a}

Defined in

Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Isometric

Cited by

1 results in Mathlib

Foundations

Depth 232 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonUnitalNormedRingStarRingNormedSpaceIsScalarTowerSMulCommClassPartialOrderStarOrderedRingNonnegSpectrumClassNonUnitalIsometricContinuousFunctionalCalculusContinuousStarCompleteSpace