ON SMOOTH, NONLINEAR SURJECTIONS OF BANACH-SPACES

Authors
BATES SM
Citation
Sm. Bates, ON SMOOTH, NONLINEAR SURJECTIONS OF BANACH-SPACES, Israel Journal of Mathematics, 100, 1997, pp. 209-220
Citations number
15
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Israel Journal of Mathematics → ACNP
ISSN journal
00212172
Volume
100
Year of publication
1997
Pages
209 - 220
Database
ISI
SICI code
0021-2172(1997)100:<209:OSNSOB>2.0.ZU;2-H
Abstract
It is shown that (1) every infinite-dimensional Banach space admits a C-1 Lipschitz map onto any separable Banach space, and (2) if the dual of a separable Banach space X contains a normalized, weakly null Bana ch-Saks sequence, then X admits a C-infinity map onto any separable Ba nach space. Subsequently, we generalize these results to mappings onto larger target spaces.