Theorems · Definition · functional analysis

CFC.abs

{A : Type u_2} →
  [inst : NonUnitalRing A] →
    [inst_1 : StarRing A] →
      [inst_2 : TopologicalSpace A] →
        [inst_3 : Module ℝ A] →
          [inst_4 : SMulCommClass ℝ A A] →
            [inst_5 : IsScalarTower ℝ A A] →
              [NonUnitalContinuousFunctionalCalculus ℝ A IsSelfAdjoint] →
                [inst_7 : PartialOrder A] → [StarOrderedRing A] → [NonnegSpectrumClass ℝ A] → A → A

The absolute value defined via the non-unital continuous functional calculus.

Defined in

Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs

Cited by

43 results in Mathlib

Foundations

Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonUnitalRingStarRingTopologicalSpaceModuleSMulCommClassIsScalarTowerNonUnitalContinuousFunctionalCalculusPartialOrderStarOrderedRingNonnegSpectrumClass