Quotients of continuous convex functions on nonreflexive Banach spaces

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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.
5 pages

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Functional Analysis, 46B10; 46B03

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http://salesiana.dossiersoluciones.com/handle/123456789/129855

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0706.0633
 http://arxiv.org/abs/0706.0633

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arXiv