Characterisations of the weak expectation property

TL;DR

This paper explores different ways to characterize the weak expectation property (WEP) in C*-algebras using operator system representations, providing new insights related to Connes' embedding problem.

Contribution

It introduces novel characterizations of WEP through operator system quotients, connecting to longstanding problems in operator algebra theory.

Findings

New formulations of WEP via operator system quotients

Connections established between WEP and Connes' embedding problem

Enhanced understanding of operator system representations in C*-algebras

Abstract

We use representations of operator systems as quotients to deduce various characterisations of the weak expectation property (WEP) for C?*-algebras. By Kirchberg's work on WEP, these results give new formulations of Connes' embedding problem.