Best constants for Lipschitz embeddings of metric spaces into c_0

Details Best constants for Lipschitz embeddings of metric spaces into c_0 Best constants for Lipschitz embeddings of metric spaces into c_0

2007-08-29

arxiv.org/abs/0708.3924v1

Mathematics

Functional Analysis

22 pages

Scientific paper

We answer a question of Aharoni by showing that every separable metric space can be Lipschitz 2-embedded into $c_0$ and this result is sharp; this improves earlier estimates of Aharoni, Assouad and Pelant. We use our methods to examine the best constant for Lipschitz embeddings of the classical $\ell_p-$spaces into $c_0$ and give other applications. We prove that if a Banach space embeds almost isometrically into $c_0$, then it embeds linearly almost isometrically into $c_0$. We also study Lipschitz embeddings into $c_0^+$.

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