Operator-Valued Kirchberg Theory

TL;DR

This paper extends Kirchberg's categorical approach to define and analyze new notions of WEP and QWEP relative to C*-algebras, exploring their properties, examples, and applications to C*-norms.

Contribution

It introduces relative WEP and QWEP concepts based on Kirchberg's categorical perspective, expanding the classical theory with new properties and examples.

Findings

New notions of relative WEP and QWEP established

Examples illustrating relations with classical WEP and QWEP provided

Applications to recent results on C*-norms demonstrated

Abstract

In this paper, we will follow Kirchberg's categorical perspective to establish new notions of WEP and QWEP relative to a C$^*$-algebra, and develop similar properties as in the classical WEP and QWEP. Also we will show some examples of relative WEP and QWEP to illustrate the relations with the classical cases. Finally we will apply our notions to recent results on C$^*$-norms.