Theorems · Definition · functional analysis

CFC.conjSqrt

{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] → [SeparatelyContinuousMul A] → A → A →L[ℝ] A

Conjugation by the square root of an element, i.e. sqrt c * a * sqrt c.

Defined in

Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.ConjSqrt

Cited by

13 results in Mathlib

Foundations

Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderRingStarRingTopologicalSpaceStarOrderedRingAlgebraContinuousFunctionalCalculusNonnegSpectrumClassSeparatelyContinuousMul