Theorems · Theorem · functional analysis

RCLike.nonUnitalContinuousFunctionalCalculus

∀ {𝕜 : Type u_1} {A : Type u_2} [inst : RCLike 𝕜] [inst_1 : NonUnitalNormedRing A] [inst_2 : StarRing A]
  [inst_3 : NormedSpace 𝕜 A] [inst_4 : IsScalarTower 𝕜 A A] [inst_5 : SMulCommClass 𝕜 A A] [inst_6 : StarModule 𝕜 A]
  {p : A → Prop} {p₁ : Unitization 𝕜 A → Prop},
  (∀ {x : A}, p₁ ↑x ↔ p x) →
    ∀ [ClosedEmbeddingContinuousFunctionalCalculus 𝕜 (Unitization 𝕜 A) p₁] [CompleteSpace A] [CStarRing A],
      NonUnitalContinuousFunctionalCalculus 𝕜 A p

Defined in

Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances

Cited by

2 results in Mathlib

Foundations

Depth 232 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNonUnitalNormedRingStarRingNormedSpaceIsScalarTowerSMulCommClassStarModuleClosedEmbeddingContinuousFunctionalCalculusCompleteSpaceCStarRing