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ArticleOriginal scientific text

Title

An almost nowhere Fréchet smooth norm on superreflexive spaces

Authors 1, 2

Affiliations

  1. Mathematical Institute, Czech Academy of Sciences, Žitná 25, CZ-11567 Praha, Czech Republic.
  2. Institut für Mathematik, Johannes Kepler Universität, Altenbergerstr. A-4040 Linz, Austria

Abstract

Every separable infinite-dimensional superreflexive Banach space admits an equivalent norm which is Fréchet differentiable only on an Aronszajn null set.

Keywords

ENG
Aronszajn null, convex, differentiable, Banach space

Bibliography

  1. [A] N. Aronszajn, Differentiability of Lipschitzian mappings between Banach spaces, Studia Math. 57 (1976), 147-190.
  2. [BL] Y. Benyamini and J. Lindenstrauss, Geometric non-linear functional analysis, to appear.
  3. [C] M. Csörnyei, Aronszajn null and Gaussian null sets coincide, to appear.
  4. [D] J. Diestel, Geometry of Banach Spaces, Springer, Berlin, 1975.
  5. [K] P. L. Konyagin, On points of existence and nonuniqueness of elements of best approximation, in: Theory of Functions and its Applications, P. L. Ul'yanov (ed.), Izdat. Moskov. Univ., 1986, 38-43 (in Russian).
  6. [Man] P. Mankiewicz, On the differentiability of Lipschitz mappings in Fréchet spaces, Studia Math. 45 (1973), 15-29.
  7. [MM] J. Matoušek and E. Matoušková, A highly non-smooth norm on Hilbert space, Israel J. Math., to appear.
  8. [M1] E. Matoušková, Convexity and Haar null sets, Proc. Amer. Math. Soc. 125 (1997), 1793-1799.
  9. [M2] E. Matoušková, The Banach-Saks property and Haar null sets, Comment. Math. Univ. Carolin. 39 (1998), 71-80.
  10. [PT] D. Preiss and J. Tišer, Two unexpected examples concerning differentiability of Lipschitz functions on Banach spaces, in: Geometric Aspects of Functional Analysis, Israel Seminar (GAFA), J. Lindenstrauss and V. Milman (eds.), Birkhäuser, 1995, 219-238.
  11. [PZ] D. Preiss and L. Zajíček, Stronger estimates of smallness of sets of Fréchet nondifferentiability of convex functions, Suppl. Rend. Circ. Mat. Palermo (2) 3 (1984), 219-223.
Studia Mathematica
1999/133/1
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Pages:
93-99
Main language of publication
English
Received
1998-04-17
Accepted
1998-06-16
Published
1999
Exact and natural sciences