Theorems · Theorem · functional analysis

cfcUnits_pow

∀ {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] [inst_9 : ContinuousFunctionalCalculus R A p]
  [inst_10 : ContinuousInv₀ R] (f : R → R) (a : A) (hf' : ∀ x ∈ spectrum R a, f x ≠ 0) (n : ℕ)
  (hf : autoParam (ContinuousOn f (spectrum R a)) cfcUnits_pow._auto_1) (ha : autoParam (p a) cfcUnits_pow._auto_3),
  cfcUnits f a hf' hf ha ^ n = cfcUnits (fun i => f i ^ n) a ⋯ ⋯ ha

Defined in

Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital

Cited by

1 results in Mathlib

Foundations

Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemifieldStarRingMetricSpaceIsTopologicalSemiringContinuousStarTopologicalSpaceRingStarRingAlgebraContinuousFunctionalCalculusContinuousInv₀