Ondřej Kurka
Abstract
If a separable Banach space contains an isometric copy of every separable reflexive Fréchet 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 Fréchet smooth dual space. This improves a result of G. Godefroy and N. J. Kalton.
A significance statement is not available in the OpenAlex record.
A contribution statement is not available in the OpenAlex record.
Method details are not available in the OpenAlex metadata.
Findings are not separately available in the OpenAlex metadata.
Limitations are not available in the OpenAlex metadata.
Application details are not available in the OpenAlex metadata.
If a separable Banach space contains an isometric copy of every separable reflexive Fréchet 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 Fréchet smooth dual space. This improves a result of G. Godefroy and N. J. Kalton.
Key concepts: Separable space, Banach space, Mathematics, Pure mathematics, Banach manifold, Space (punctuation), Fréchet space, Interpolation space