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

Abstract

Very recently, Špakula 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 $p=1$.

arXiv commentFinal version, published in Journal of Mathematical Analysis and Application

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• Quasi-Locality and Property A
• Structure and $K$-theory of ${\ell }^p$ uniform Roe algebras
• Persistence approximation property for $L^p$ operator algebras
• Quasi-locality for étale groupoids
• $L^p$ coarse Baum-Connes conjecture via $C_0$ coarse geometry