Relative Commutant Pictures of Roe Algebras

Jan Spakula, Aaron Peter Tikuisis (Corresponding Author)

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)1019-1048
Number of pages30
JournalCommunications in Mathematical Physics
Volume365
Issue number3
Early online date30 Jan 2019
DOIs
Publication statusPublished - Feb 2019

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Commutant
algebra
operators
Algebra
Operator
Asymptotic Dimension
Uniform Algebra
metric space
Commute
Straight
Metric space
Tend
Oscillation
decomposition
Decompose
oscillations

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 journalArticle

Spakula, Jan ; Tikuisis, Aaron Peter. / Relative Commutant Pictures of Roe Algebras. In: Communications in Mathematical Physics. 2019 ; Vol. 365, No. 3. pp. 1019-1048.
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