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Quotients of Continuous Convex Functions on Nonreflexive Banach Spaces

P. Holický, O. F. K. Kalenda, L. Veselý, L. Zajíček (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

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 also gives a stronger version of Klee's result concerning renormings of nonreflexive spaces and non-norm-attaining functionals.

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