Theorems · Definition · functional analysis

cfcUnits

{R : Type u_1} →
  {A : Type u_2} →
    {p : A → Prop} →
      [inst : Semifield 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] →
                        [ContinuousFunctionalCalculus R A p] →
                          [ContinuousInv₀ R] →
                            (f : R → R) →
                              (a : A) →
                                (∀ x ∈ spectrum R a, f x ≠ 0) →
                                  autoParam (ContinuousOn f (spectrum R a)) cfcUnits._auto_1 →
                                    autoParam (p a) cfcUnits._auto_3 → Aˣ

Bundle cfc f a into a unit given a proof that f is nonzero on the spectrum of a.

Defined in

Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital

Cited by

6 results in Mathlib

Foundations

Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemifieldStarRingMetricSpaceIsTopologicalSemiringContinuousStarTopologicalSpaceRingStarRingAlgebraContinuousFunctionalCalculusContinuousInv₀