Tensor products of function systems revisited

TL;DR

This paper revisits tensor products of function systems, providing explicit descriptions of their positive cones and new approximation theorems for nuclear maps, simplifying existing characterizations.

Contribution

It offers an explicit description of positive cones in maximal tensor products and introduces an approximation theorem for nuclear maps between function systems.

Findings

Explicit description of positive cones in maximal tensor products

An approximation theorem for nuclear maps

Elementary proofs of known characterizations of nuclear function systems

Abstract

Based on the Archimedeanization developed by Paulsen and Tomforde, we give an explicit description for the positive cones of maximal tensor products of function systems. From this description, we obtain an approximation theorem for nuclear maps between function systems. As an application, we give elementary proofs on several characterizations of nuclear function systems that are already known.