Quotients of continuous convex functions on nonreflexive Banach spaces

Details Quotients of continuous convex functions on nonreflexive Banach spaces Quotients of continuous convex functions on nonreflexive Banach spaces

2007-06-05

arxiv.org/abs/0706.0633v1

Mathematics

Functional Analysis

5 pages

Scientific paper

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.

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