Abstract
| 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 | |
| Publication status | Published - Feb 2019 |
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ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
Cite this
Relative Commutant Pictures of Roe Algebras. / Spakula, Jan; Tikuisis, Aaron Peter (Corresponding Author).
In: Communications in Mathematical Physics, Vol. 365, No. 3, 02.2019, p. 1019-1048.Research output: Contribution to journal › Article
}
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 -