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Espaces de Banach superstables, distances stables et homeomorphismes uniformes

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Abstract

We introduce here the notion of superstable Banach space, as the superproperty associated with the stability property of J. L. Krivine and B. Maurey. IfE is superstable, so are theL p(E) for eachp∈[1, +∞[. If the Banach spaceX uniformly imbeds into a superstable Banach space, then there exists an equivalent invariant superstable distance onX; as a consequenceX contains subspaces isomorphic tol pspaces (for somep∈[1, ∞[). We give also a generalization of a result of P. Enflo: the unit ball ofc 0 does not uniformly imbed into any stable Banach space.

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Authors and Affiliations

  1. U.E.R. de Mathématique et Informatique Laboratoire “Théories Géométriques”, Université Paris VII, 2 Place Jussieu, 75251, Paris, Cedex 05, France

    Yves Raynaud

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  1. Yves Raynaud
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Raynaud, Y. Espaces de Banach superstables, distances stables et homeomorphismes uniformes. Israel J. Math. 44, 33–52 (1983). https://doi.org/10.1007/BF02763170

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  • DOI: https://doi.org/10.1007/BF02763170

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