Quotients of continuous convex functions on nonreflexive Banach spaces

• Autorzy: Holicky P. , Kalenda O. F. , Vesely L. , Zajícek L.
• Języki publikacji: EN

Abstrakty

EN

On each nonreflexive Banach space X there exists a positive continuous convex function ƒ such that 1/ƒ is not a d.c. function (i.e., a difference of two continuous convex functions). This result together with known ones implies that X is reflexive if and only if each everywhere defined quotient of two continuous convex functions is a d.c. function. Our construction also gives a stronger version of Klee's result concerning renormings of nonreflexive spaces and non-norm-attaining functionals.

Słowa kluczowe

EN

reflexivity; dc functions; non-norm-attaining functionals; renormings

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2007
• Tom: Vol. 55, no 3
• Strony: 211--217
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Holicky P.

autor

Kalenda O. F.

autor

Vesely L.

autor

Zajícek L.

• Faculty of Mathematics and Physics, Charles University, Sokolovska 83, 18675 Praha 8, Czech Republic,

Bibliografia

• [1] D. van Dulst, Reflexive and Superreflexive Banach Spaces, Math. Centre Tracts 102, Math. Centrum, Amsterdam, 1978.
• [2] P. Hartman, On functions representable as a difference of convex functions, Pacific J. Math. 9 (1959), 707-713.
• [3] J.-B. Hiriart-Urruty, Generalized differentiability, duality and optimization for problems dealing with differences of convex functions, in: Convexity and Duality in Optimization (Groningen, 1984), Lecture Notes in Econom. and Math. Systems 256, Springer, Berlin, 1985, 37-70.
• [4] R. C. James, Characterizations of reflexivity, Studia Math. 23 (1964), 205-216.
• [5] V. L. Klee, Jr., Some characterizations of reflexivity, Rev. Ci. Lima 52 (1950), 15-23.
• [6] R. E. Megginson, An Introduction to Banach Space Theory, Grad. Texts in Math. 183, Springer, New York, 1998.
• [7] L. Vesely and L. Zajicek, On compositions of delta-convex mappings and functions, preprint, http://arxiv.org/abs/0706.0624, 2007.