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arXiv · 2002.05394

Exactness and SOAP of Crossed Products via Herz--Schur multipliers

Andrew McKee·Lyudmila Turowska
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Abstract

Given a $C^*$-dynamical system $(A,G,\alpha)$, with $G$ a discrete group, Schur $A$-multipliers and Herz--Schur $(A,G,\alpha)$-multipliers are used to implement approximation properties, namely exactness and the strong operator approximation property (SOAP), of $A \rtimes_{\alpha , r} G$. The resulting characterisations of exactness and SOAP of $A \rtimes_{\alpha , r} G$ generalise the corresponding statements for the reduced group $C^*$-algebra.

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Andrew McKee, Lyudmila Turowska. 2020-02-13. Exactness and SOAP of Crossed Products via Herz--Schur multipliers. https://arxiv.org/abs/2002.05394

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