Jiménez Sevilla, María del Mar and Sánchez González, Luis (2011) Smooth extension of functions on a certain class of nonseparable Banach spaces. Journal of Mathematical Analysis and Applications, 378 (1). pp. 173183. ISSN 0022247X

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Abstract
Let us consider a Banach space X with the property that every realvalued Lipschitz function f can be uniformly approximated by a Lipschitz, C1smooth function g with Lip(g)⩽CLip(f) (with C depending only on the space X). This is the case for a Banach space X biLipschitz homeomorphic to a subset of c0(Γ), for some set Γ, such that the coordinate functions of the homeomorphism are C1smooth (Hájek and Johanis, 2010 . Then, we prove that for every closed subspace Y⊂X and every C1smooth (Lipschitz) function f:Y→R, there is a C1smooth (Lipschitz, respectively) extension of f to X. We also study C1smooth extensions of realvalued functions defined on closed subsets of X. These results extend those given in Azagra et al. (2010) [4] to the class of nonseparable 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 12:54 
Last Modified:  06 Feb 2014 09:54 
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