Relative Commutant Pictures of Roe Algebras

Jan Spakula; Aaron Peter Tikuisis

doi:10.1007/s00220-019-03313-x

Relative Commutant Pictures of Roe Algebras

Jan Spakula, Aaron Peter Tikuisis (Corresponding Author)

Mathematical Science

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

3 Downloads (Pure)

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 -propogation (in the sense of Roe) for every > 0. These descriptions hold both for the usual Roe algebra and for the uniform Roe algebra.

Original language	English
Pages (from-to)	1019-1048
Number of pages	30
Journal	Communications in Mathematical Physics
Volume	365
Issue number	3
Early online date	30 Jan 2019
DOIs	https://doi.org/10.1007/s00220-019-03313-x
Publication status	Published - Feb 2019

Access to Document

10.1007/s00220-019-03313-xLicence: Unspecified

Accepted Manuscript
This is a post-peer-review, pre-copyedit version of an article published in Communications in Mathematical Physics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00220-019-03313-x
Accepted author manuscript, 430 KBLicence: Unspecified
Spakula_etal_sv_relative_commutant_AAM
This is a post-peer-review, pre-copyedit version of an article published in Communications in Mathematical Physics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00220-019-03313-x
Accepted author manuscript, 430 KB

Link to publication in Scopus

Fingerprint Dive into the research topics of 'Relative Commutant Pictures of Roe Algebras'. Together they form a unique fingerprint.

Cite this

@article{4052a6ffaa7c4ca9afdbfc69f9f96fe2,

title = "Relative Commutant Pictures of Roe Algebras",

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 -propogation (in the sense of Roe) for every > 0. These descriptions hold both for the usual Roe algebra and for the uniform Roe algebra. ",

author = "Jan Spakula and Tikuisis, {Aaron Peter}",

note = "AT was supported by EPSRC EP/N00874X/1. JS was supported by Marie Curie FP7-PEOPLE-2013-CIG Coarse Analysis (631945). We would like to thank Ulrich Bunke, Alexander Engel, John Roe, Thomas Weighill, Stuart White, and Rufus Willett for comments and discussion relating to this piece.",

year = "2019",

month = feb,

doi = "10.1007/s00220-019-03313-x",

language = "English",

volume = "365",

pages = "1019--1048",

journal = "Communications in Mathematical Physics",

issn = "0010-3616",

publisher = "Springer ",

number = "3",

}

TY - JOUR

T1 - Relative Commutant Pictures of Roe Algebras

AU - Spakula, Jan

AU - Tikuisis, Aaron Peter

N1 - AT was supported by EPSRC EP/N00874X/1. JS was supported by Marie Curie FP7-PEOPLE-2013-CIG Coarse Analysis (631945). We would like to thank Ulrich Bunke, Alexander Engel, John Roe, Thomas Weighill, Stuart White, and Rufus Willett for comments and discussion relating to this piece.

PY - 2019/2

Y1 - 2019/2

N2 - 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 -propogation (in the sense of Roe) for every > 0. These descriptions hold both for the usual Roe algebra and for the uniform Roe algebra.

AB - 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 -propogation (in the sense of Roe) for every > 0. These descriptions hold both for the usual Roe algebra and for the uniform Roe algebra.

UR - http://www.scopus.com/inward/record.url?scp=85062105450&partnerID=8YFLogxK

U2 - 10.1007/s00220-019-03313-x

DO - 10.1007/s00220-019-03313-x

M3 - Article

VL - 365

SP - 1019

EP - 1048

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -