Crossed products of C*-algebras with the weak expectation property

TL;DR

This paper establishes that for amenable group actions on unital C*-algebras, the crossed product retains the weak expectation property if and only if the original algebra has it, clarifying the property’s behavior under such constructions.

Contribution

It proves an if-and-only-if condition for the weak expectation property to be preserved in crossed products under amenable group actions.

Findings

Crossed product has WEP iff original algebra has WEP for amenable actions

Clarifies the behavior of WEP under crossed product constructions

Provides a characterization of WEP preservation in this context

Abstract

If $\alpha$ is an amenable action of a discrete group $G$ on a unital C*-algebra $A$, then the crossed-product C*-algebra $A\rtimes_\alpha G$ has the weak expectation property if and only if $A$ has this property.