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Genericity of Fréchet smooth spaces

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Abstract

If a separable Banach space X contains an isometric copy of every separable reflexive Fréchet smooth Banach space, then X contains an isometric copy of every separable Banach space. The same conclusion holds if we consider separable Banach spaces with Fréchet smooth dual space. This improves a result of G. Godefroy and N.J. Kalton.

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Authors and Affiliations

  1. Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Prague 8, Czech Republic

    Ondřej Kurka

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  1. Ondřej Kurka
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Kurka, O. Genericity of Fréchet smooth spaces. RACSAM 106, 371–406 (2012). https://doi.org/10.1007/s13398-012-0063-9

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  • DOI: https://doi.org/10.1007/s13398-012-0063-9

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