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arXiv · 2309.11391

On stability of metric spaces and Kalton's property $Q$

F. Baudier·Th. Schlumprecht·A. Zsák
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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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F. Baudier, Th. Schlumprecht, A. Zsák. 2023-09-20. On stability of metric spaces and Kalton's property $Q$. https://arxiv.org/abs/2309.11391

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