We answer a question of Aharoni by showing that every separable metric space can be Lipschitz 2-embedded into c₀ 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 -spaces into c₀ and give other applications. We prove that if a Banach space embeds almost isometrically into c₀, then it embeds linearly almost isometrically into c₀. We also study Lipschitz embeddings into c₀⁺.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm199-3-4,
author = {N. J. Kalton and G. Lancien},
title = {Best constants for Lipschitz embeddings of metric spaces into c0},
journal = {Fundamenta Mathematicae},
volume = {201},
year = {2008},
pages = {249-272},
zbl = {1153.46047},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm199-3-4}
}
N. J. Kalton; G. Lancien. Best constants for Lipschitz embeddings of metric spaces into c₀. Fundamenta Mathematicae, Tome 201 (2008) pp. 249-272. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm199-3-4/