Property A and the operator norm localization property for discrete metric spaces

TL;DR

This paper explores the relationship between property A and the operator norm localization property in discrete metric spaces, establishing their equivalence under certain conditions relevant to coarse geometry and operator K-theory.

Contribution

It proves the equivalence of property A and the operator norm localization property for discrete metric spaces with bounded geometry.

Findings

Property A and the operator norm localization property are equivalent for discrete spaces with bounded geometry.

The results have implications for coarse geometry and operator K-theory.

The paper clarifies the relationship between two important coarse geometric properties.

Abstract

We study property A defined by G. Yu and the operator norm localization property defined by X. Chen, R. Tessera, X. Wang, and G. Yu. These are coarse geometric properties for metric spaces which have applications to operator K-theory. It is proved that the two properties are equivalent for discrete metric spaces with bounded geometry.