Jiménez Sevilla, María Del MarSánchez González, Luis2023-06-202023-06-2020110022-247X10.1016/j.jmaa.2010.12.057https://hdl.handle.net/20.500.14352/41997Let 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.engjournal articlehttp://www.sciencedirect.com/science/journal/0022247Xopen access517.98Smooth extensionsSmooth approximationsAnálisis funcional y teoría de operadores