2007/06/05 by P. Holicky, Petr Holický, O. Kalenda +8
Computer Science · Mathematics · #46B03 #46B10 #Advanced Banach Space Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Optimization and Variational Analysis #math.FA #msc:46B03 #msc:46B10
paper · pdf · doi:10.48550/arxiv.0706.0633
5 pages
arxiv created 2007/06/05 · openalex publication_date 2007/06/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.