English

Genericity of Fr\'echet smooth spaces

Functional Analysis 2012-09-12 v1

Abstract

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

Keywords

Cite

@article{arxiv.1109.5726,
  title  = {Genericity of Fr\'echet smooth spaces},
  author = {Ondřej Kurka},
  journal= {arXiv preprint arXiv:1109.5726},
  year   = {2012}
}

Comments

34 pages

R2 v1 2026-06-21T19:10:41.223Z