Best constants for Lipschitz embeddings of metric spaces into $c_0$
Volume 199 / 2008
Fundamenta Mathematicae 199 (2008), 249-272
MSC: Primary 46B20; Secondary 46T99.
DOI: 10.4064/fm199-3-4
Abstract
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 $c_0^+$.
