Banach spaces determined by their uniform structures

William B. Johnson; Joram Lindenstrauss; Gideon Schechtman

Banach spaces determined by their uniform structures

Functional Analysis 2009-09-25 v1

Authors: William B. Johnson , Joram Lindenstrauss , Gideon Schechtman

Abstract

Following results of Bourgain and Gorelik we show that the spaces $\ell_p$ , $1<p<\infty$ , 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 $c_0$ , then it is isomorphic to $c_0$ . We show also that there are Banach spaces which are uniformly homeomorphic to exactly $2$ isomorphically distinct spaces.

Keywords

banach space properties banach spaces banach algebras

Cite

@article{arxiv.math/9701203,
  title  = {Banach spaces determined by their uniform structures},
  author = {William B. Johnson and Joram Lindenstrauss and Gideon Schechtman},
  journal= {arXiv preprint arXiv:math/9701203},
  year   = {2009}
}

Banach spaces determined by their uniform structures

Abstract

Keywords

Cite

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