On stability of metric spaces and Kalton's property Q

2023/09/20 by Baudier, F., Schlumprecht, Th., Zsák, A.
#05C63 #46B20 #46B85 #51F30 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2309.11391

Abstract

The first named author introduced the notion of upper stability for metric spaces as a relaxation of stability. The motivation was a search for a new invariant to distinguish the class of reflexive Banach spaces from stable metric spaces in the coarse and uniform category. In this paper we show that property Q does in fact imply upper stability. We also provide a direct proof of the fact that reflexive spaces are upper stable by relating the latter notion to the asymptotic structure of Banach spaces.

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