Abstract of a paper by P. Holicky, O. Kalenda, L. Vesely, and L. Zajicek
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 The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0706.0633 or http://arXiv.org/abs/0706.0633 or by email in unzipped form by transmitting an empty message with subject line uget 0706.0633 or in gzipped form by using subject line get 0706.0633 to: math@arXiv.org.
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Dale Alspach