Best constants for Lipschitz embeddings of metric spaces into c₀

N. J. Kalton, and G. Lancien. "Best constants for Lipschitz embeddings of metric spaces into c₀." Fundamenta Mathematicae 199.3 (2008): 249-272. <http://eudml.org/doc/283239>.

@article{N2008,
abstract = {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 $ℓ_p$-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⁺.},
author = {N. J. Kalton, G. Lancien},
journal = {Fundamenta Mathematicae},
keywords = {Lipschitz embedding; almost isometric embedding},
language = {eng},
number = {3},
pages = {249-272},
title = {Best constants for Lipschitz embeddings of metric spaces into c₀},
url = {http://eudml.org/doc/283239},
volume = {199},
year = {2008},
}

TY - JOUR
AU - N. J. Kalton
AU - G. Lancien
TI - Best constants for Lipschitz embeddings of metric spaces into c₀
JO - Fundamenta Mathematicae
PY - 2008
VL - 199
IS - 3
SP - 249
EP - 272
AB - 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 $ℓ_p$-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⁺.
LA - eng
KW - Lipschitz embedding; almost isometric embedding
UR - http://eudml.org/doc/283239
ER -