A quasi-local characterisation of $L^p$-Roe algebras

Kang Li; Zhijie Wang; Jiawen Zhang

doi:10.1016/j.jmaa.2019.02.013

A quasi-local characterisation of $L^p$-Roe algebras

Functional Analysis 2019-03-04 v3 Metric Geometry Operator Algebras

Authors: Kang Li , Zhijie Wang , Jiawen Zhang

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Abstract

Very recently, \v{S}pakula and Tikuisis provide a new characterisation of (uniform) Roe algebras via quasi-locality when the underlying metric spaces have straight finite decomposition complexity. In this paper, we improve their method to deal with the $L^p$ -version of (uniform) Roe algebras for any $p\in [1,\infty)$ . Due to the lack of reflexivity on $L^1$ -spaces, some extra work is required for the case of $p=1$ .

Keywords

l^p-roe algebras quasi-locality uniform roe algebras finite decomposition complexity metric spaces reflexivity

Cite

@article{arxiv.1808.08593,
  title  = {A quasi-local characterisation of $L^p$-Roe algebras},
  author = {Kang Li and Zhijie Wang and Jiawen Zhang},
  journal= {arXiv preprint arXiv:1808.08593},
  year   = {2019}
}

Comments

Final version, published in Journal of Mathematical Analysis and Application

A quasi-local characterisation of $L^p$-Roe algebras

Abstract

Keywords

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