1Faculty of Mathematics and Physics Charles University Sokolovská 83 186 75 Praha 8, Czech Republic 2Faculty of Mathematics and Physics Charles University Sokolovská 83 186 75, Praha 8 Czech Republic 3Dipartimento 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
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.
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
Affiliations des auteurs :
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
@article{10_4064_ba55_3_3,
author = {P. Holick\'y and O. F. K. Kalenda and L. Vesel\'y and L. Zaj{\'\i}\v{c}ek},
title = {Quotients of {Continuous} {Convex} {Functions} on {Nonreflexive} {Banach} {Spaces}},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
pages = {211--217},
year = {2007},
volume = {55},
number = {3},
doi = {10.4064/ba55-3-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ba55-3-3/}
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AU - P. Holický
AU - O. F. K. Kalenda
AU - L. Veselý
AU - L. Zajíček
TI - Quotients of Continuous Convex Functions on Nonreflexive Banach Spaces
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2007
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%J Bulletin of the Polish Academy of Sciences. Mathematics
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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
