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We give several sufficient conditions on a pair of Banach spaces X and Y under which each Lipschitz mapping from a domain in X to Y has, for every ǫ > 0, a point of ǫ-Fréchet differentiability. Most of these conditions are stated in terms of the moduli of asymptotic smoothness and convexity, notions which appeared in the literature under a variety of names.… (More)

- Jean Bourgain, Joram Lindenstrauss
- Discrete & Computational Geometry
- 1993

- Vladimir P. Fonf, Joram Lindenstrauss, Libor Vesely
- Journal of Approximation Theory
- 2011

In the theory of Banach spaces a rather small class of spaces has always played a central role (actually even before the formulation of the general theory). This class —the class of classical Banach spaces— contains the L p (p) spaces (p a measure , 1 < p < °°) and the C(K) spaces (K compact Hausdorff) and some related spaces. These spaces are very… (More)

Lipschitz quotient mappings and uniform quotient mappings between Banach spaces are introduced and investigated. In particular, it is shown that if a Banach space is a uniform quotient of L p , 1 < p < ∞, then it is isomorphic to a linear quotient of L p. For the purpose of studying quotient mappings and also for their own interest, new concepts related to… (More)

- J Lindenstrauss, E Matou Skovv, D Preiss, E Matou Skov A, And D Preiss
- 2007

We give two examples that in innnite dimensional Ba-nach spaces the measure-null sets are not preserved by Lipschitz homeomorphisms. There exists a closed set D ` 2 which contains a translate of any compact set in the unit ball of`2 and a Lips-chitz isomorphism F of`2 ontò 2 so that F(D) is contained in a hyperplane. Let X be a Banach space with an… (More)

- Vladimir P. Fonf, Joram Lindenstrauss, Libor Vesely
- Journal of Approximation Theory
- 2014

Corrigendum Corrigendum to " Best approximation in polyhedral Banach spaces " [J. Abstract The present note is a corrigendum to the paper " Best approximation in polyhedral Banach spaces " , J. Professor G. Godefroy kindly pointed out to us that the implication " if P Y is H-u.s.c. on its effective domain then Y is relatively strongly proximinal " in [1,… (More)

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