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 -