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The structure of uniformly Gâteaux smooth Banach spaces

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Abstract

It is shown that a Banach spaceX admits an equivalent uniformly Gâteaux smooth norm if and only if the dual ball ofX* in its weak star topology is a uniform Eberlein compact.

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Authors and Affiliations

  1. Mathematical Institute, Czech Academy of Sciences, Žitná 25, 11567, Praha 1, Czech Republic

    Marián Fabian & Václav Zizler

  2. Equipe d’Analyse, Université Paris VI, Boite 186, 4, Place Jussieu, 75252, Paris Cedex 05, France

    Gilles Godefroy

  3. Department of Mathematics, University of Alberta, T6G 2G1, Edmonton, Canada

    Václav Zizler

Authors
  1. Marián Fabian
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  2. Gilles Godefroy
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  3. Václav Zizler
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Corresponding author

Correspondence to Marián Fabian.

Additional information

Supported by AV 101-97-02, AV 1019003 and GA ČR 201-98-1449.

Supported by GA ČR 201-98-1449, AV 1019003 and GAUK 1/1998.

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Fabian, M., Godefroy, G. & Zizler, V. The structure of uniformly Gâteaux smooth Banach spaces. Isr. J. Math. 124, 243–252 (2001). https://doi.org/10.1007/BF02772620

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  • DOI: https://doi.org/10.1007/BF02772620

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