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Relative commutant pictures of Roe algebras

Relative commutant pictures of Roe algebras
Relative commutant pictures of Roe algebras

Let X be a proper metric space, which has finite asymptotic dimension in the sense of Gromov (or more generally, straight finite decomposition complexity of Dranishnikov and Zarichnyi). New descriptions are provided of the Roe algebra of X: (i) it consists exactly of operators which essentially commute with diagonal operators coming from Higson functions (that is, functions on X whose oscillation tends to 0 at ∞), and (ii) it consists exactly of quasi-local operators, that is, ones which have finite ϵ-propogation (in the sense of Roe) for every ϵ> 0. These descriptions hold both for the usual Roe algebra and for the uniform Roe algebra.

0010-3616
1019-1048
Špakula, Ján
c43164e4-36a7-4372-9ce2-9bfbba775d77
Tikuisis, Aaron
8c8d8bda-16c5-4c7e-a9d7-5a01c4968a63
Špakula, Ján
c43164e4-36a7-4372-9ce2-9bfbba775d77
Tikuisis, Aaron
8c8d8bda-16c5-4c7e-a9d7-5a01c4968a63

Špakula, Ján and Tikuisis, Aaron (2019) Relative commutant pictures of Roe algebras. Communications in Mathematical Physics, 365 (3), 1019-1048. (doi:10.1007/s00220-019-03313-x).

Record type: Article

Abstract

Let X be a proper metric space, which has finite asymptotic dimension in the sense of Gromov (or more generally, straight finite decomposition complexity of Dranishnikov and Zarichnyi). New descriptions are provided of the Roe algebra of X: (i) it consists exactly of operators which essentially commute with diagonal operators coming from Higson functions (that is, functions on X whose oscillation tends to 0 at ∞), and (ii) it consists exactly of quasi-local operators, that is, ones which have finite ϵ-propogation (in the sense of Roe) for every ϵ> 0. These descriptions hold both for the usual Roe algebra and for the uniform Roe algebra.

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More information

Submitted date: 2017
Accepted/In Press date: 8 November 2018
e-pub ahead of print date: 30 January 2019
Published date: February 2019

Identifiers

Local EPrints ID: 420958
URI: http://eprints.soton.ac.uk/id/eprint/420958
ISSN: 0010-3616
PURE UUID: 35d213ef-6f56-4ea1-9547-d1a1f850bfaf
ORCID for Ján Špakula: ORCID iD orcid.org/0000-0001-5775-9905

Catalogue record

Date deposited: 18 May 2018 16:31
Last modified: 17 Dec 2019 05:28

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