Every separable infinite-dimensional superreflexive Banach space admits an equivalent norm which is Fréchet differentiable only on an Aronszajn null set.
Mathematical Institute, Czech Academy of Sciences, Žitná 25, CZ-11567 Praha, Czech Republic.
Institut für Mathematik, Johannes Kepler Universität, Altenbergerstr. A-4040 Linz, Austria
Bibliografia
[A] N. Aronszajn, Differentiability of Lipschitzian mappings between Banach spaces, Studia Math. 57 (1976), 147-190.
[BL] Y. Benyamini and J. Lindenstrauss, Geometric non-linear functional analysis, to appear.
[C] M. Csörnyei, Aronszajn null and Gaussian null sets coincide, to appear.
[D] J. Diestel, Geometry of Banach Spaces, Springer, Berlin, 1975.
[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).
[Man] P. Mankiewicz, On the differentiability of Lipschitz mappings in Fréchet spaces, Studia Math. 45 (1973), 15-29.
[MM] J. Matoušek and E. Matoušková, A highly non-smooth norm on Hilbert space, Israel J. Math., to appear.
[M1] E. Matoušková, Convexity and Haar null sets, Proc. Amer. Math. Soc. 125 (1997), 1793-1799.
[M2] E. Matoušková, The Banach-Saks property and Haar null sets, Comment. Math. Univ. Carolin. 39 (1998), 71-80.
[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.
[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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv133i1p93bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.