A new proof of Fréchet differentiability of Lipschitz functions

Abstract

We give a relatively simple (self-contained) proof that every real-valued Lipschitz function on l2 (or more generally on an Asplund space) has points of Frechet differentiability. Somewhat more generally, we show that a real-valued Lipschitz function on a separable Banach space has points of Frechet differentiability provided that the w * closure of the set of its points of Gâteaux differentiability is norm separable.