A note on differentiability of Lipschitz maps

• Autorzy: Górak R.
• 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 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.

Słowa kluczowe

EN

Lipschitz map; Gateaux and Frechet differentiability; scattered spaces

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2010
• Tom: Vol. 58, no 3
• Strony: 259--268
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Górak R.

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

Bibliografia

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