Theorems · Theorem · functional analysis

cfcHom_mem_elemental

∀ {𝕜 : Type u_1} {A : Type u_2} {p : A → Prop} [inst : RCLike 𝕜] [inst_1 : Ring A] [inst_2 : StarRing A]
  [inst_3 : Algebra 𝕜 A] [inst_4 : TopologicalSpace A] [inst_5 : StarModule 𝕜 A]
  [inst_6 : ContinuousFunctionalCalculus 𝕜 A p] [inst_7 : IsTopologicalRing A] [inst_8 : ContinuousStar A] {a : A}
  (ha : p a) (f : C(↑(spectrum 𝕜 a), 𝕜)), (cfcHom ha) f ∈ StarAlgebra.elemental 𝕜 a

Defined in

Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Range

Cited by

2 results in Mathlib

Foundations

Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeRingStarRingAlgebraTopologicalSpaceStarModuleContinuousFunctionalCalculusIsTopologicalRingContinuousStar