Embeddings of matrix algebras into uniform Roe algebras and quasi-local algebras

2023/10/05 by Ozawa, Narutaka · 2 citations
#05C48 #46L05 #47C15 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2310.03677

Abstract

We answer the recent problem posed by Baudier, Braga, Farah, Vignati, and Willett that asks whether the ℓ_∞-direct sum of the matrix algebras embeds into the uniform Roe algebra or the quasi-local algebra of a uniformly locally finite metric space. The answers are no and yes, respectively. Hence the inclusion of the uniform Roe algebra into the quasi-local algebra can be proper.

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