# 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

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topLindenstrauss, 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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