Authors: | Braga, Bruno M. Farah, Ilijas Vignati, Alessandro |
Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | Operator norm localization property for equi-approximable families of projections | Journal: | Journal of Noncommutative Geometry | Volume: | 18 | Issue: | 2 | First page: | 657 | Last page: | 680 | Issue Date: | 1-Jan-2024 | Rank: | ~M22 | ISSN: | 1661-6952 | DOI: | 10.4171/JNCG/555 | Abstract: | The rigidity problem for uniform Roe algebras was recently positively solved. Before its solution was found, there were positive solutions under the assumption of certain technical geometric conditions. In this paper, we introduce weaker versions of the operator norm localization property (ONL) which turn out to characterize those technical geometric conditions. We use this to obtain new rigidity results for nonmetrizable coarse spaces. As an application, we provide a novel partial answer to a question of White and Willett about Cartan subalgebras of uniform Roe algebras. We also study embeddings between uniform Roe algebras. |
Keywords: | coarse geometry | operator norm localization property | uniform Roe algebras | Publisher: | European Mathematical Society Publishing House |
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