A Note on Differentiability of Lipschitz Maps

Volume 58 / 2010

Rafa/l Górak Bulletin Polish Acad. Sci. Math. 58 (2010), 259-268 MSC: 46G05, 58C20, 54G12. DOI: 10.4064/ba58-3-8


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.


  • Rafa/l GórakTechnical University of Warsaw
    Pl. Politechniki 1
    00-661 Warszawa, Poland

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