A new proof of Fréchet differentiability of Lipschitz functions

Joram Lindenstrauss; David Preiss

Journal of the European Mathematical Society (2000)

  • Volume: 002, Issue: 3, page 199-216
  • ISSN: 1435-9855

Abstract

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We give a relatively simple (self-contained) proof that every real-valued Lipschitz function on ℓ 2 (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.

How to cite

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Lindenstrauss, Joram, and Preiss, David. "A new proof of Fréchet differentiability of Lipschitz functions." Journal of the European Mathematical Society 002.3 (2000): 199-216. <http://eudml.org/doc/277259>.

@article{Lindenstrauss2000,
abstract = {We give a relatively simple (self-contained) proof that every real-valued Lipschitz function on $\ell _2$ (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.},
author = {Lindenstrauss, Joram, Preiss, David},
journal = {Journal of the European Mathematical Society},
keywords = {Lipschitz function; Fréchet differentiability; Gâteaux differentiability; Lipschitz function; Fréchet differentiability},
language = {eng},
number = {3},
pages = {199-216},
publisher = {European Mathematical Society Publishing House},
title = {A new proof of Fréchet differentiability of Lipschitz functions},
url = {http://eudml.org/doc/277259},
volume = {002},
year = {2000},
}

TY - JOUR
AU - Lindenstrauss, Joram
AU - Preiss, David
TI - A new proof of Fréchet differentiability of Lipschitz functions
JO - Journal of the European Mathematical Society
PY - 2000
PB - European Mathematical Society Publishing House
VL - 002
IS - 3
SP - 199
EP - 216
AB - We give a relatively simple (self-contained) proof that every real-valued Lipschitz function on $\ell _2$ (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.
LA - eng
KW - Lipschitz function; Fréchet differentiability; Gâteaux differentiability; Lipschitz function; Fréchet differentiability
UR - http://eudml.org/doc/277259
ER -

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