This is an announcement for the paper "Smooth extension of functions on non-separable Banach spaces" by Mar Jimenez-Sevilla and Luis Sanchez-Gonzalez.

Abstract: Let us consider a Banach space $X$ with the property that every Lipschitz function can be uniformly approximated by Lipschitz and $C^1$-smooth functions (this is the case either for a weakly compactly generated Banach space $X$ with a $C^1$-smooth norm, or a Banach space $X$ bi-Lipschitz homeomorphic to a subset of $c_0(\Gamma)$, for some set $\Gamma$, such that the coordinate functions of the homeomorphism are $C^1$-smooth). Then for every closed subspace $Y\subset X$ and every $C^1$-smooth (Lipschitz) function $f:Y\to\Real$, there is a $C^1$-smooth (Lipschitz, repectively) extension of $f$ to $X$. An analogous result can be stated for real-valued functions defined on closed convex subsets of $X$.

Archive classification: math.FA

Mathematics Subject Classification: 46B20

Remarks: 12 pages

The source file(s), draftSmoothextension220210.tex: 59770 bytes, is(are) stored in gzipped form as 1002.4147.gz with size 15kb. The corresponding postcript file has gzipped size 84kb.

Submitted from: lfsanche@mat.ucm.es

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