Quotients of continuous convex functions on nonreflexive Banach spaces
Functional Analysis
2007-06-06 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0706.0633,
title = {Quotients of continuous convex functions on nonreflexive Banach spaces},
author = {P. Holicky and O. Kalenda and L. Vesely and L. Zajicek},
journal= {arXiv preprint arXiv:0706.0633},
year = {2007}
}
Comments
5 pages