Hostname: page-component-6898cfcb55-kwdml Total loading time: 0 Render date: 2026-11-11T06:05:38.442Z Has data issue: false hasContentIssue false
  • English
  • Français

Almost Fréchet differentiability of finitely many Lipschitz functions

Part of:Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  26 February 2010

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

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.

MSC classification

Secondary:46B20: Geometry and structure of normed linear spaces

Information

Type
Research Article
Information
Mathematika , Volume 43 , Issue 2 , December 1996, pp. 393 - 412
Copyright
Copyright © University College London 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

A.Aronszajn, N.. Differentiability of Lipschitz functions in Banach spaces. Studia Math., 57 (1976), 147–160.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), 29–39.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), 225–251.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), 430–470.CrossRefGoogle Scholar
M.Mankiewicz, P.. On the differentiability of Lipschitz mappings in Fréchet spaces. Studia Math., 45 (1973), 15–29.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), 219–238.Google Scholar