Isometric embeddings of compact spaces into Banach spaces

Yves Dutrieux; Gilles Lancien

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arXiv · 0801.2486

Isometric embeddings of compact spaces into Banach spaces

Yves Dutrieux·Gilles Lancien

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Abstract

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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BibTeX RIS

Yves Dutrieux, Gilles Lancien. 2008-01-16. Isometric embeddings of compact spaces into Banach spaces. https://arxiv.org/abs/0801.2486

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