Theorems · Definition · functional analysis

PositiveLinearMap.ofPreGNS

{A : Type u_1} → [inst : NonUnitalCStarAlgebra A] → [inst_1 : PartialOrder A] → (f : A →ₚ[ℂ] ℂ) → f.PreGNS ≃ₗ[ℂ] A

The map from the GNS space to the C⋆-algebra, as a linear equivalence.

Defined in

Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal

Cited by

8 results in Mathlib

Foundations

Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonUnitalCStarAlgebraPartialOrder