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-subspaces of stablep-Banach spaces, 0<p≦1 |
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Authors: | J Bastero |
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Institution: | 1. Dpto. de Teoria de Funciones, Facultad de Ciencias de la. Universidad de Zaragoza, Zaragoza, Spain
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Abstract: | Each infinite dimensional subspace ofL p (0<p≦1) is shown to contain a copy of somel q p≦q<∞, using arguments similar to the ones that appearin Krivine and Maurey's paper concerning stable Banach spaces. Generally speaking, ifX is a stable infinite dimensionalp-Banach space, with 0<p≦1, then, there exists aq(p≦q<∞), such that,X contains (1+ε)-isomorphic copies ofl q , for all ε>0. Moreover, it is possible to prove that if a stablep-Banach space, 0<p≦1, contains an isomorphic copy ofl q,p≦q<∞, then, it also contains (1+ε) -isomorphic copies ofl q , for all ε>0. |
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