An almost nowhere Fréchet smooth norm on superreflexive spaces

• Autorzy: Eva Matoušková
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

Aronszajn null; convex; differentiable; Banach space

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 133
• Numer: 1
• Strony: 93-99

Daty

wydano

1999

otrzymano

1998-04-17

poprawiono

1998-06-16

Twórcy

autor

Eva Matoušková

• 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.