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January, 2021 The approximation property and exactness of locally compact groups
Yuhei SUZUKI
J. Math. Soc. Japan 73(1): 263-275 (January, 2021). DOI: 10.2969/jmsj/83368336

Abstract

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

Funding Statement

This work was supported by JSPS KAKENHI Grant-in-Aid for Young Scientists (Start-up, No. 17H06737) and tenure track funds of Nagoya University.

Citation

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Yuhei SUZUKI. "The approximation property and exactness of locally compact groups." J. Math. Soc. Japan 73 (1) 263 - 275, January, 2021. https://doi.org/10.2969/jmsj/83368336

Information

Received: 23 September 2019; Published: January, 2021
First available in Project Euclid: 9 September 2020

Digital Object Identifier: 10.2969/jmsj/83368336

Subjects:
Primary: 22D25
Secondary: 46L05, 46L55

Rights: Copyright © 2021 Mathematical Society of Japan

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Vol.73 • No. 1 • January, 2021
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