Theorems · Theorem · functional analysis

cfc_sum

∀ {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] {ι : Type u_3}
  (f : ι → R → R) (a : A) (s : Finset ι),
  autoParam (∀ i ∈ s, ContinuousOn (f i) (spectrum R a)) cfc_sum._auto_1 → cfc (∑ i ∈ s, f i) a = ∑ i ∈ s, cfc (f i) a

Defined in

Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital

Cited by

1 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringStarRingMetricSpaceIsTopologicalSemiringContinuousStarTopologicalSpaceRingStarRingAlgebraContinuousFunctionalCalculus