Quotients of continuous convex functions on nonreflexive Banach spaces

Autor:	Holicky, P., Kalenda, O., Vesely, L., Zajicek, L.
Rok vydání:	2007
Předmět:	Mathematics - Functional Analysis 46B10 46B03
Druh dokumentu:	Working Paper
Popis:	On each nonreflexive Banach space X there exists a positive continuous convex function f such that 1/f 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 gives also a stronger version of Klee's result concerning renormings of nonreflexive spaces and non-norm-attaining functionals. Comment: 5 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0706.0633 Zobrazit plný text záznamu View this record from Arxiv