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arXiv · 1311.4584

Low distortion embeddings into Asplund Banach spaces

Antonín Procházka·Luis Sánchez-González
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Abstract

We give a simple example of a countable metric space $M$ that does not embed bi-Lipschitz with distortion strictly less than 2 into any Asplund space. Actually, if $M$ embeds with distortion strictly less than 2 to a Banach space $X$, then $X$ contains an isomorphic copy of $\ell_1$. We also show that the space $M$ does not embed with distortion strictly less than $2$ into $\ell_1$ itself but it does embed isometrically into a space that is isomorphic to $\ell_1$.

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Antonín Procházka, Luis Sánchez-González. 2013-11-18. Low distortion embeddings into Asplund Banach spaces. https://arxiv.org/abs/1311.4584

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