Theorems · Definition · functional analysis

cfcL

{R : Type u_1} →
  {A : Type u_2} →
    {p : A → Prop} →
      [inst : CommSemiring R] →
        [inst_1 : StarRing R] →
          [inst_2 : MetricSpace R] →
            [inst_3 : IsTopologicalSemiring R] →
              [inst_4 : ContinuousStar R] →
                [inst_5 : TopologicalSpace A] →
                  [inst_6 : Ring A] →
                    [inst_7 : StarRing A] →
                      [inst_8 : Algebra R A] →
                        [instCFC : ContinuousFunctionalCalculus R A p] → {a : A} → p a → C(↑(spectrum R a), R) →L[R] A

cfcHom bundled as a continuous linear map.

Defined in

Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital

Cited by

8 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringStarRingMetricSpaceIsTopologicalSemiringContinuousStarTopologicalSpaceRingStarRingAlgebraContinuousFunctionalCalculus