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Almost Fréchet differentiability of finitely many Lipschitz functions

Published online by Cambridge University Press:  26 February 2010

J. Lindenstrauss
Affiliation:
Department of Mathematics, Hebrew University, Jerusalem, Israel.
D. Preiss
Affiliation:
Department of Mathematics, University College London, LondonWC1E 6BT.
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Extract

This paper is a contribution to the general problem of differentiability of Lipschitz functions between Banach spaces. We establish here a result concerning the existence of derivatives which are in some sense between the notions of Gâteaux and Frechet differentiability.

Type
Research Article
Copyright
Copyright © University College London 1996

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References

A.Aronszajn, N.. Differentiability of Lipschitz functions in Banach spaces. Studia Math., 57 (1976), 147160.CrossRefGoogle Scholar
BJLPS.Bates, S. M.Johnson, W. B.Lindenstrauss, J.Preiss, D. and Schechtmann, G.. Uniform quotient spaces. To appear.Google Scholar
C.Christensen, J. P. R.. Measure theoretic zero sets in infinitely dimensional spaces and application to differentiability of Lipschitz mappings. Actes du Deuzieme Colloque d'Analyse Fonctionele de Bordeaux, 2 (1973), 2939.Google Scholar
DGZ.Deville, R.Godefroy, G. and Zizler, V.. Smoothness and renormings in Banach spaces (Pitman Monographs #64, 1993).Google Scholar
HM.Heinrich, S. and Mankiewicz, P.. Applications of ultrapowers to the uniform and Lipschitz classification of Banach spaces. Studia Math., 73 (1982), 225251.CrossRefGoogle Scholar
I.Ives, D.. Thesis (University College London, to be submitted).Google Scholar
JLS.Johnson, W. B.Lindenstrauss, J. and Schechtmann, G.. Banach spaces determined by their uniform structures. Geometric and Functional Analysis, 6 (1996), 430470.CrossRefGoogle Scholar
M.Mankiewicz, P.. On the differentiability of Lipschitz mappings in Fréchet spaces. Studia Math., 45 (1973), 1529.CrossRefGoogle Scholar
P.Preiss, D.. Differentiability of Lipschitz functions on Banach spaces. J. Fund. Anal., 91 (1990), 213, 345.CrossRefGoogle Scholar
PT.Preiss, D. and Tiser, J.. Two unexpected examples concerning differentiability of Lipschitz functions on Banach spaces. Operator Theory: Advances and Applications, 77 (1995), 219238.Google Scholar