This is an announcement for the paper "Quotients of continuous convex functions on nonreflexive Banach spaces" by P. Holicky, O. Kalenda, L. Vesely, and L. Zajicek.
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.
Archive classification: math.FA
Mathematics Subject Classification: 46B10; 46B03
Remarks: 5 pages
The source file(s), 06HKVZscisly.tex: 19081 bytes, is(are) stored in gzipped form as 0706.0633.gz with size 7kb. The corresponding postcript file has gzipped size 71kb.
Submitted from: zajicek@karlin.mff.cuni.cz
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