Exactness and SOAP of Crossed Products via Herz-Schur multipliers

Journal article, 2021

Given a C*-dynamical system (A,G,α), with G a discrete group, Schur A-multipliers and Herz–Schur (A,G,α)-multipliers are used to implement approximation properties, namely exactness and the strong operator approximation property (SOAP), of A⋊α,rG. The resulting characterisations of exactness and SOAP of A⋊α,rG generalise the corresponding statements for the reduced group C*-algebra.