Banach spaces determined by their uniform structures

1997/01/17 by William B. Johnson, Joram Lindenstrauss, Johnson, William B. +3
Mathematics · #46B20 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA #msc:46B20

paper · pdf · doi:10.48550/arxiv.math/9701203

arxiv created 1997/01/17 · openalex publication_date 1997/01/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Following results of Bourgain and Gorelik we show that the spaces ℓ_p, 1<p<∞, as well as some related spaces have the following uniqueness property: If X is a Banach space uniformly homeomorphic to one of these spaces then it is linearly isomorphic to the same space. We also prove that if a C(K) space is uniformly homeomorphic to c₀, then it is isomorphic to c₀. We show also that there are Banach spaces which are uniformly homeomorphic to exactly 2 isomorphically distinct spaces.

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