Theorems · Theorem · functional analysis

NonUnitalClosedEmbeddingContinuousFunctionalCalculus.isClosedEmbedding

∀ {R : Type u_1} {A : Type u_2} {p : outParam (A → Prop)} {inst : CommSemiring R} {inst_1 : Nontrivial R}
  {inst_2 : StarRing R} {inst_3 : MetricSpace R} {inst_4 : IsTopologicalSemiring R} {inst_5 : ContinuousStar R}
  {inst_6 : NonUnitalRing A} {inst_7 : StarRing A} {inst_8 : TopologicalSpace A} {inst_9 : Module R A}
  {inst_10 : IsScalarTower R A A} {inst_11 : SMulCommClass R A A}
  [self : NonUnitalClosedEmbeddingContinuousFunctionalCalculus R A p] (a : A) (ha : p a),
  Topology.IsClosedEmbedding ⇑(cfcₙHom ha)

Defined in

Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital

Cited by

1 results in Mathlib

Foundations

Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonUnitalClosedEmbeddingContinuousFunctionalCalculus