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