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A Banach space admits a locally uniformly rotund norm if its dual is a Vašák space

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Abstract

LetV be a Banach space whose dualV * is Vašák, that is, weakly countably determined. Then an equivalent locally uniformly rotund norm onV is constructed. According to a recent example of Mercourakis, this is a real extension of an earlier result of Godefroy Troyanski, Whitfield and Zizler, whereV * has been a subspace of a weakly compactly generated Banach space.

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Authors and Affiliations

  1. Sibeliova 49, 162 00, Prague 6, Czechoslovakia

    Marián Fabian & Stanimir Troyanski

  2. Department of Mathematics and Informatics, University of Sofia, 5, Boullevard A. Ivanou, 1126, Sofia, Bulgaria

    Marián Fabian & Stanimir Troyanski

Authors
  1. Marián Fabian
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  2. Stanimir Troyanski
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Dedicated to the memory of Zdeněk Frolík

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Fabian, M., Troyanski, S. A Banach space admits a locally uniformly rotund norm if its dual is a Vašák space. Israel J. Math. 69, 214–224 (1990). https://doi.org/10.1007/BF02937305

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  • DOI: https://doi.org/10.1007/BF02937305

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