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A note on differentiability of Lipschitz maps

Górak R.

Bulletin of the Polish Academy of Sciences. Mathematics

2010

Vol. 58, no 3

259-268

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 Frechet 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 Gateaux differentiable.