Joram Lindenstrauss

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New concepts related to approximating a Lipschitz function between Banach spaces by aane functions are introduced. Results which clarify when such approximations are possible are proved and in some cases a complete characterization of the spaces X, Y for which any Lipschitz function from X to Y can be so approximated is obtained. This is applied to the(More)
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)
We give several suucient 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 > 0, a point of-Fr echet diierentiability. 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. We(More)