Smooth approximations

0345050 - MÚ 2011 RIV US eng J - Journal Article
Hájek, Petr Pavel - Johanis, M.
Smooth approximations.
Journal of Functional Analysis. Roč. 259, č. 3 (2010), s. 561-582. ISSN 0022-1236. E-ISSN 1096-0783
R&D Projects: GA AV ČR IAA100190801
Institutional research plan: CEZ:AV0Z10190503
Keywords : C-P-smooth * Banach spaces * Lipschitz
Subject RIV: BA - General Mathematics
Impact factor: 1.196, year: 2010
http://www.sciencedirect.com/science/article/pii/S0022123610001795

We prove, among other things, that a Lipschitz (or uniformly continuous) mapping f X -> Y can be approximated (even in a fine topology) by smooth Lipschitz (rest). uniformly continuous) mapping, if X is a separable Banach space admitting a smooth Lipschitz bump and either X or Y is a separable C (K) space (rest) super-reflexive space) Further. we show how smooth approximation of Lipschitz mappings is closely related to a smooth approximation of C-1-smooth mappings together with then first derivatives. As a corollary we obtain new results on smooth approximation of C-1-smooth mappings together with their first derivatives.
Permanent Link: http://hdl.handle.net/11104/0186415