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Genericity of Fréchet smooth spaces

  • Ondřej Kurka
Orignal Paper

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.

Keywords

Fréchet smoothness Isometrically universal Banach space Monotone basis Effros–Borel structure Well-founded tree 

Mathematics Subject Classification (2000)

Primary: 46B04 46B20 Secondary: 46B15 54H05 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of Mathematical Analysis, Faculty of Mathematics and PhysicsCharles UniversityPrague 8Czech Republic

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