Work

On Stability of Metric Spaces and Kalton’s Property Q

Year: 2024

Type: article

Abstract: ABSTRACT The first named author introduced the notion of upper stability for metric spaces in F. Baudier, Barycentric gluing and geometry of stable metrics, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 116 no. 1, (2022), 48 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: The Quarterly Journal of Mathematics

DOI: 10.1093/qmath/haae050

Authors: F Baudier, Th Schlumprecht, A ZSÁK

Institutions: Texas A&M University, Czech Technical University in Prague, University of Cambridge

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,184

Funder: National Science Foundation