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Sous-espaces de L

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Abstract

A typical result of the paper isTheorem. LetE be a reflexive subspace ofL 1 (Ω, A, P) [(Ω,A, P) a probability space]. IfE contains a subspace isomorphic to lp then for every ε > 0,E contains a subspace (1 + ε) isomorphic to lp.

The technics are probability theory and ultraproducts.

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Bibliographie

  1. D. Dacunha-Castelle,Variables échangeables et espaces d’Orlicz, Séminaire Maurey-Schwartz, Ecole Polytechnique, Paris, 1974–75.

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  2. D. Dacunha-Castelle et J. L. Krivine,Applications des ultraproduits aux espaces de Banach, Studia Math.41 (1972), 315–334.

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  3. J. L. Krivine,Sous-espaces de dimension finie des espaces de Banach réticulés (à paraître).

  4. J. Lindenstrauss et L. Tzafriri,On Orlicz sequences spaces. I. Israel J. Math.10 (1971), 379–390.

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  5. J. Neveu,Bases mathématiques du calcul des probabilités, Masson, Paris.

  6. M. Kadec et A. Pelczynski,Bases, lacunary sequences and complemented subspaces in the spaces L p, Studia Math.21 (1962), 161–176.

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  7. D. Dacunha-Castelle et J. L. Krivine,Sur les sous-espaces de L 1 C. R. Acad. Sci. Paris,280 (1975), 645–648.

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Authors and Affiliations

  1. Centre d’Orsay Mathématique, Université de Paris Sud, 91405, Orsay Cédex, France

    D. Dacunha-Castelle & J. L. Krivine

Authors
  1. D. Dacunha-Castelle
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  2. J. L. Krivine
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Additional information

Dans [7], il est annoncé, de façon incorrecte, la démonstration de (C); en fait il est seulement démontré que (C) ⇔ (C′) (voir plus loin l’énoncé de la conjecture (C′)).

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Dacunha-Castelle, D., Krivine, J.L. Sous-espaces de L. Israel J. Math. 26, 320–351 (1977). https://doi.org/10.1007/BF03007651

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  • DOI: https://doi.org/10.1007/BF03007651

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