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 The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1002.4147 or http://arXiv.org/abs/1002.4147 or by email in unzipped form by transmitting an empty message with subject line uget 1002.4147 or in gzipped form by using subject line get 1002.4147 to: math@arXiv.org.