Year: 2024
Type: article
Abstract: The first named author introduced the notion of upper stability for metric spaces in [2] 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.
Source: Apollo (University of Cambridge)
DOI: 10.17863/cam.111953
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6887944128
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