A Note on Differentiability of Lipschitz Maps
Volume 58 / 2010
Bulletin Polish Acad. Sci. Math. 58 (2010), 259-268
MSC: 46G05, 58C20, 54G12.
DOI: 10.4064/ba58-3-8
Abstract
We show that every Lipschitz map defined on an open subset of the Banach space $C(K)$, where $K$ is a scattered compactum, with values in a Banach space with the Radon–Nikodym property, has a point of Fréchet differentiability. This is a strengthening of the result of Lindenstrauss and Preiss who proved that for countable compacta. As a consequence of the above and a result of Arvanitakis we prove that Lipschitz functions on certain function spaces are Gâteaux differentiable.
