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A quasi-local characterisation of $L^p$-Roe algebras (1808.08593v3)

Published 26 Aug 2018 in math.FA, math.MG, and math.OA

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 $Lp$-version of (uniform) Roe algebras for any $p\in [1,\infty)$. Due to the lack of reflexivity on $L1$-spaces, some extra work is required for the case of $p=1$.

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