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Quasi-local algebras and asymptotic expanders

Quasi-local algebras and asymptotic expanders
Quasi-local algebras and asymptotic expanders
In this paper, we study the relation between the uniform Roe algebra and the uniform quasi-local algebra associated to a metric space of bounded geometry. In the process, we introduce a weakening of the notion of expanders, called asymptotic expanders. We show that being a sequence of asymptotic expanders is a coarse property under certain connectedness condition, and it implies non-uniformly local amenability. Moreover, we also analyse some C∗-algebraic properties of uniform quasi-local algebras. In particular, we show that a uniform quasi-local algebra is nuclear if and only if the underlying metric space has Property A.
1661-7207
Spakula, Jan
c43164e4-36a7-4372-9ce2-9bfbba775d77
Zhang, Jiawen
aa149f14-dd1d-42b0-b863-623d1fedd1f5
Nowak, Piotr
d86850e8-5309-4f78-abf0-73d2036249b1
Li, Kang
62945651-4b08-4fa3-a1fa-0eadaddbf6c5
Spakula, Jan
c43164e4-36a7-4372-9ce2-9bfbba775d77
Zhang, Jiawen
aa149f14-dd1d-42b0-b863-623d1fedd1f5
Nowak, Piotr
d86850e8-5309-4f78-abf0-73d2036249b1
Li, Kang
62945651-4b08-4fa3-a1fa-0eadaddbf6c5

Spakula, Jan, Zhang, Jiawen, Nowak, Piotr and Li, Kang (2020) Quasi-local algebras and asymptotic expanders. Groups, Geometry, and Dynamics. (In Press)

Record type: Article

Abstract

In this paper, we study the relation between the uniform Roe algebra and the uniform quasi-local algebra associated to a metric space of bounded geometry. In the process, we introduce a weakening of the notion of expanders, called asymptotic expanders. We show that being a sequence of asymptotic expanders is a coarse property under certain connectedness condition, and it implies non-uniformly local amenability. Moreover, we also analyse some C∗-algebraic properties of uniform quasi-local algebras. In particular, we show that a uniform quasi-local algebra is nuclear if and only if the underlying metric space has Property A.

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QUASI-LOCAL ALGEBRAS - Accepted Manuscript
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More information

Accepted/In Press date: 2 April 2020

Identifiers

Local EPrints ID: 440785
URI: http://eprints.soton.ac.uk/id/eprint/440785
ISSN: 1661-7207
PURE UUID: 83e4f748-f37d-4c68-ba1b-82cdcc22a187
ORCID for Jan Spakula: ORCID iD orcid.org/0000-0001-5775-9905

Catalogue record

Date deposited: 18 May 2020 16:34
Last modified: 07 Oct 2020 02:04

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Contributors

Author: Jan Spakula ORCID iD
Author: Jiawen Zhang
Author: Piotr Nowak
Author: Kang Li

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