Geodesic
Quotients of Continuous Convex Functions on Nonreflexive Banach Spaces
P. Holický1 ; O. F. K. Kalenda2 ; L. Veselý3 ; L. Zajíček2
1 Faculty of Mathematics and Physics Charles University Sokolovská 83 186 75 Praha 8, Czech Republic
2 Faculty of Mathematics and Physics Charles University Sokolovská 83 186 75, Praha 8 Czech Republic
3 Dipartimento di Matematica “F. Enriques” Università degli Studi di Milano Via C. Saldini 50 20133 Milano, Italy
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) no. 3, pp. 211-217.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ba55-3-3
Keywords: each nonreflexive banach space there exists positive continuous convex function function difference continuous convex functions result together known implies reflexive only each everywhere defined quotient continuous convex functions function construction gives stronger version klees result concerning renormings nonreflexive spaces non norm attaining functionals

P. Holický 1 ; O. F. K. Kalenda 2 ; L. Veselý 3 ; L. Zajíček 2

1 Faculty of Mathematics and Physics Charles University Sokolovská 83 186 75 Praha 8, Czech Republic
2 Faculty of Mathematics and Physics Charles University Sokolovská 83 186 75, Praha 8 Czech Republic
3 Dipartimento di Matematica “F. Enriques” Università degli Studi di Milano Via C. Saldini 50 20133 Milano, Italy 
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     title = {Quotients of  {Continuous} {Convex} {Functions} on {Nonreflexive} {Banach} {Spaces}},
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P. Holický; O. F. K.  Kalenda; L. Veselý; L. Zajíček. Quotients of  Continuous Convex Functions on Nonreflexive Banach Spaces. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) no. 3, pp. 211-217. doi : 10.4064/ba55-3-3. http://geodesic.mathdoc.fr/articles/10.4064/ba55-3-3/

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