A Note on Differentiability of Lipschitz Maps

• Autorzy: Rafał Górak
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 58C20: Differentiation theory (Gateaux, Fr\'echet, etc.)
• 54G12: Scattered spaces
• 46G05: Derivatives

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2010
• Tom: 58
• Numer: 3
• Strony: 259-268

Daty

wydano

2010

Twórcy

autor

Rafał Górak

• Technical University of Warsaw, Pl. Politechniki 1, 00-661 Warszawa, Poland

Identyfikatory

DOI

10.4064/ba58-3-8