Isometric embeddings of compact spaces into Banach spaces

Details Isometric embeddings of compact spaces into Banach spaces Isometric embeddings of compact spaces into Banach spaces

2008-01-16

arxiv.org/abs/0801.2486v1

Mathematics

Functional Analysis

8 pages

Scientific paper

We show the existence of a compact metric space $K$ such that whenever $K$ embeds isometrically into a Banach space $Y$, then any separable Banach space is linearly isometric to a subspace of $Y$. We also address the following related question: if a Banach space $Y$ contains an isometric copy of the unit ball or of some special compact subset of a separable Banach space $X$, does it necessarily contain a subspace isometric to $X$? We answer positively this question when $X$ is a polyhedral finite-dimensional space, $c_0$ or $\ell_1$.

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