Theorems · Definition · functional analysis

CFC.rpow

{A : Type u_1} →
  [inst : PartialOrder A] →
    [inst_1 : Ring A] →
      [inst_2 : StarRing A] →
        [inst_3 : TopologicalSpace A] →
          [StarOrderedRing A] →
            [inst_5 : Algebra ℝ A] →
              [ContinuousFunctionalCalculus ℝ A IsSelfAdjoint] → [NonnegSpectrumClass ℝ A] → A → ℝ → A

Real powers of operators, based on the unital continuous functional calculus.

Defined in

Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic

Cited by

7 results in Mathlib

Foundations

Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderRingStarRingTopologicalSpaceStarOrderedRingAlgebraContinuousFunctionalCalculusNonnegSpectrumClass