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arXiv · 1901.07430

The approximation property and exactness of locally compact groups

Yuhei Suzuki
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Abstract

We extend a theorem of Haagerup and Kraus in the C*-algebra context: for a locally compact group with the approximation property (AP), the reduced C*-crossed product construction preserves the strong operator approximation property (SOAP). In particular their reduced group C*-algebras have the SOAP. Our method also solves another open problem: the AP implies exactness for general locally compact groups.

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BibTeXRIS

Yuhei Suzuki. 2019-01-16. The approximation property and exactness of locally compact groups. https://doi.org/10.2969/jmsj%2F83368336

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