Theorems · Definition · functional analysis

CFC.sqrt

{A : Type u_1} →
  [inst : PartialOrder A] →
    [inst_1 : NonUnitalRing A] →
      [inst_2 : TopologicalSpace A] →
        [inst_3 : StarRing A] →
          [inst_4 : Module ℝ A] →
            [inst_5 : SMulCommClass ℝ A A] →
              [inst_6 : IsScalarTower ℝ A A] →
                [StarOrderedRing A] →
                  [NonUnitalContinuousFunctionalCalculus ℝ A IsSelfAdjoint] → [NonnegSpectrumClass ℝ A] → A → A

Square roots of operators, based on the non-unital continuous functional calculus.

Defined in

Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic

Cited by

82 results in Mathlib

Foundations

Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderNonUnitalRingTopologicalSpaceStarRingModuleSMulCommClassIsScalarTowerStarOrderedRingNonUnitalContinuousFunctionalCalculusNonnegSpectrumClass