Banach Spaces Determined by Their Uniform Structures

  title={Banach Spaces Determined by Their Uniform Structures},
  author={William B. Johnson and Joram Lindenstrauss and Gideon Schechtman},
Following results of Bourgain and Gorelik we show that the spaces lp, 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. Subject… CONTINUE READING
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