Authors
Citation
G. Godefroy et al., The Banach space c(0) is determined by its metric, CR AC S I, 327(9), 1998, pp. 817-822
Citations number
13
Categorie Soggetti
Mathematics
Journal title
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE
ISSN journal
07644442
→ ACNP
Volume
327
Issue
9
Year of publication
1998
Pages
817 - 822
Database
ISI
SICI code
0764-4442(199811)327:9<817:TBSCID>2.0.ZU;2-V
Abstract
In this Note we show that a Banach space which is Lipschitz-isomorphic to a
subspace of c(0) is linearly isomorphic to a subspace of c(0). We deduce t
hat a space which is Lipschitz-isomorphic to c(0) is in fact linearly isomo
rphic to c(0). We also prove that a space which is uniformly homeomorphic t
o a subspace of c(0) has a summable Szlenk index. Finally, we investigate t
he extension of these results to the non-separable case. (C) Academie des S
ciences/Elsevier, Paris.