Theorems · Definition · functional analysis

PositiveLinearMap.toPreGNS

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

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

Defined in

Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal

Cited by

5 results in Mathlib

Foundations

Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonUnitalCStarAlgebraPartialOrder