We show that, given a Banach space X, the Lipschitz-free space over X, denoted by ℱ(X), is isomorphic to . Some applications are presented, including a nonlinear version of Pełczyński’s decomposition method for Lipschitz-free spaces and the identification up to isomorphism between ℱ(ℝⁿ) and the Lipschitz-free space over any compact metric space which is locally bi-Lipschitz embeddable into ℝⁿ and which contains a subset that is Lipschitz equivalent to the unit ball of ℝⁿ. We also show that ℱ(M) is isomorphic to ℱ(c₀) for all separable metric spaces M which are absolute Lipschitz retracts and contain a subset which is Lipschitz equivalent to the unit ball of c₀. This class includes all C(K) spaces with K infinite compact metric (Dutrieux and Ferenczi (2006) already proved that ℱ(C(K)) is isomorphic to ℱ(c₀) for those K using a different method).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm226-3-2,
author = {Pedro Levit Kaufmann},
title = {Products of Lipschitz-free spaces and applications},
journal = {Studia Mathematica},
volume = {231},
year = {2015},
pages = {213-227},
zbl = {06442705},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm226-3-2}
}
Pedro Levit Kaufmann. Products of Lipschitz-free spaces and applications. Studia Mathematica, Tome 231 (2015) pp. 213-227. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm226-3-2/