Jiménez Sevilla, María del Mar and Sánchez González, Luis (2011) Smooth extension of functions on a certain class of non-separable Banach spaces. Journal of Mathematical Analysis and Applications, 378 (1). pp. 173-183. ISSN 0022-247X
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Abstract
Let us consider a Banach space X with the property that every real-valued Lipschitz function f can be uniformly approximated by a Lipschitz, C1-smooth function g with Lip(g)⩽CLip(f) (with C depending only on the space X). This is the case for a Banach space X bi-Lipschitz homeomorphic to a subset of c0(Γ), for some set Γ, such that the coordinate functions of the homeomorphism are C1-smooth (Hájek and Johanis, 2010 . Then, we prove that for every closed subspace Y⊂X and every C1-smooth (Lipschitz) function f:Y→R, there is a C1-smooth (Lipschitz, respectively) extension of f to X. We also study C1-smooth extensions of real-valued functions defined on closed subsets of X. These results extend those given in Azagra et al. (2010) [4] to the class of non-separable Banach spaces satisfying the above property.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Smooth extensions; Smooth approximations |
| Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |
| ID Code: | 13817 |
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| Deposited On: | 10 Nov 2011 13:54 |
| Last Modified: | 10 Nov 2011 13:58 |
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