Ergodic Banach spaces |
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Authors: | Valentin Ferenczi |
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Affiliation: | Equipe d’Analyse Fonctionnelle, Université Paris 6, Boîte 186, 4, Place Jussieu, 75252 Paris Cedex 05, France |
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Abstract: | We show that any Banach space contains a continuum of non-isomorphic subspaces or a minimal subspace. We define an ergodic Banach space X as a space such that E0 Borel reduces to isomorphism on the set of subspaces of X, and show that every Banach space is either ergodic or contains a subspace with an unconditional basis which is complementably universal for the family of its block-subspaces. We also use our methods to get uniformity results. We show that an unconditional basis of a Banach space, of which every block-subspace is complemented, must be asymptotically c0 or ?p, and we deduce some new characterisations of the classical spaces c0 and ?p. |
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Keywords: | primary 46B03 secondary 03E15 |
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