Banach spaces determined by their uniform structures
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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.
author list (cited authors)
Johnson, W. B., Lindenstrauss, J., & Schechtman, G.
complete list of authors
Johnson, WB||Lindenstrauss, J||Schechtman, G