Espaces de Banach : existence et unicité de certains préduaux
Annales de l'Institut Fourier, Tome 28 (1978) no. 3, pp. 87-105.

On étudie dans ce travail le problème suivant : un espace de Banach E étant donné, existe-t-il un Banach X tel que X soit isométrique à E ? On donne un critère d’existence d’un tel espace X pour un type particulier d’espaces E. On montre ensuite qu’un tel espace X est unique à isométries près pour quelques classes d’espaces E. On en déduit alors quelques résultats sur les isométries de certains espaces de Banach et la géométrie de certains convexes compacts.

We study in this work the following problem: given a Banach space E, does there exist a Banach space X such that X be isometric to E? We give an existence criterion of such a space X for a particular type of space E. We prove that such a space X is unique, up to an isometry, for some classes of spaces E. We then deduce some results about isometries of certain Banach spaces and geometry of certain compact convex sets.

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     title = {Espaces de {Banach} : existence et unicit\'e de certains pr\'eduaux},
     journal = {Annales de l'Institut Fourier},
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Godefroy, Gilles. Espaces de Banach : existence et unicité de certains préduaux. Annales de l'Institut Fourier, Tome 28 (1978) no. 3, pp. 87-105. doi : 10.5802/aif.702. http://www.numdam.org/articles/10.5802/aif.702/

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