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Quasi-locality and Property A

Quasi-locality and Property A
Quasi-locality and Property A
Let X be a metric space with bounded geometry, , and let E be a Banach space. The main result of this paper is that either if X has Yu's Property A and , or without any condition on X when , then quasi-local operators on belong to (the appropriate variant of) the Roe algebra of X. This generalises the existing results of this type by Lange and Rabinovich, Engel, Tikuisis and the first author, and Li, Wang and the second author. As consequences, we obtain that uniform -Roe algebras (of spaces with Property A) are closed under taking inverses, and another condition characterising Property A, akin to the operator norm localisation for quasi-local operators.
0022-1236
Špakula, Ján
c43164e4-36a7-4372-9ce2-9bfbba775d77
Zhang, Jiawen
aa149f14-dd1d-42b0-b863-623d1fedd1f5
Špakula, Ján
c43164e4-36a7-4372-9ce2-9bfbba775d77
Zhang, Jiawen
aa149f14-dd1d-42b0-b863-623d1fedd1f5

Špakula, Ján and Zhang, Jiawen (2019) Quasi-locality and Property A. Journal of Functional Analysis, [108299]. (doi:10.1016/j.jfa.2019.108299).

Record type: Article

Abstract

Let X be a metric space with bounded geometry, , and let E be a Banach space. The main result of this paper is that either if X has Yu's Property A and , or without any condition on X when , then quasi-local operators on belong to (the appropriate variant of) the Roe algebra of X. This generalises the existing results of this type by Lange and Rabinovich, Engel, Tikuisis and the first author, and Li, Wang and the second author. As consequences, we obtain that uniform -Roe algebras (of spaces with Property A) are closed under taking inverses, and another condition characterising Property A, akin to the operator norm localisation for quasi-local operators.

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1809.00532 - Accepted Manuscript
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Accepted/In Press date: 9 August 2019
e-pub ahead of print date: 13 August 2019
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Identifiers

Local EPrints ID: 434004
URI: http://eprints.soton.ac.uk/id/eprint/434004
DOI: doi:10.1016/j.jfa.2019.108299
ISSN: 0022-1236
PURE UUID: 1102dd13-6492-4183-86c0-5f94aaec2507
ORCID for Ján Špakula: ORCID iD orcid.org/0000-0001-5775-9905

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Date deposited: 10 Sep 2019 16:30
Last modified: 16 Mar 2024 08:11

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Contributors

Author: Ján Špakula ORCID iD
Author: Jiawen Zhang

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