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A new proof of Fréchet differentiability of Lipschitz functions

A new proof of Fréchet differentiability of Lipschitz functions We give a relatively simple (self-contained) proof that every real-valued Lipschitz function on ℓ2 (or more generally on an Asplund space) has points of Fréchet differentiability. Somewhat more generally, we show that a real-valued Lipschitz function on a separable Banach space has points of Fréchet differentiability provided that the w * closure of the set of its points of Gâteaux differentiability is norm separable. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the European Mathematical Society Springer Journals

A new proof of Fréchet differentiability of Lipschitz functions

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Publisher
Springer Journals
Copyright
Copyright © 2000 by Springer-Verlag Berlin Heidelberg & EMS
Subject
Mathematics; Mathematics, general
ISSN
1435-9855
DOI
10.1007/s100970000019
Publisher site
See Article on Publisher Site

Abstract

We give a relatively simple (self-contained) proof that every real-valued Lipschitz function on ℓ2 (or more generally on an Asplund space) has points of Fréchet differentiability. Somewhat more generally, we show that a real-valued Lipschitz function on a separable Banach space has points of Fréchet differentiability provided that the w * closure of the set of its points of Gâteaux differentiability is norm separable.

Journal

Journal of the European Mathematical SocietySpringer Journals

Published: Aug 1, 2000

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