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
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.
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
@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},
publisher = {mathdoc},
volume = {55},
number = {3},
year = {2007},
doi = {10.4064/ba55-3-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ba55-3-3/}
}
TY - JOUR 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 SP - 211 EP - 217 VL - 55 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/ba55-3-3/ DO - 10.4064/ba55-3-3 LA - en ID - 10_4064_ba55_3_3 ER -
%0 Journal Article %A P. Holický %A O. F. K. Kalenda %A L. Veselý %A L. Zajíček %T Quotients of Continuous Convex Functions on Nonreflexive Banach Spaces %J Bulletin of the Polish Academy of Sciences. Mathematics %D 2007 %P 211-217 %V 55 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/ba55-3-3/ %R 10.4064/ba55-3-3 %G en %F 10_4064_ba55_3_3
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
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