Remarks on the operator norm localization property

Abstract

The author studies the metric spaces with operator norm localization property. It is proved that the operator norm localization property is coarsely invariant and is preserved under certain infinite union. In the case of finitely generated groups, the operator norm localization property is also preserved under the direct limits.

Keywords

Metric space / Asymptotic dimension / Operator norm localization / Coarse invariance / Roe algebra

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