Quantization in *-Algebras II: Archimedeanization

Abstract

Given a matrix quasi ordered *-vector space $${\mathcal {X}}$$ , we describe the Archimedeanization process of $${\mathcal {X}}$$ and prove some isomorphism theorems. Then, we apply these results to construct a new proof for the algebraic analog of Arveson’s extension theorem. Also we obtain an extension of Kadison’s theorem which realizes a quasi order gauged vector space as a subspace of a commutative $$C^*$$ -algebra.