Quotients of Continuous Convex Functions on Nonreflexive Banach Spaces

P. Holický, et al. "Quotients of Continuous Convex Functions on Nonreflexive Banach Spaces." Bulletin of the Polish Academy of Sciences. Mathematics 55.3 (2007): 211-217. <http://eudml.org/doc/280204>.

@article{P2007,
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 also gives a stronger version of Klee's result concerning renormings of nonreflexive spaces and non-norm-attaining functionals.},
author = {P. Holický, O. F. K. Kalenda, L. Veselý, L. Zajíček},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {reflexivity; d.c. functions; non-norm-attaining functionals; renormings},
language = {eng},
number = {3},
pages = {211-217},
title = {Quotients of Continuous Convex Functions on Nonreflexive Banach Spaces},
url = {http://eudml.org/doc/280204},
volume = {55},
year = {2007},
}

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
VL - 55
IS - 3
SP - 211
EP - 217
AB - 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.
LA - eng
KW - reflexivity; d.c. functions; non-norm-attaining functionals; renormings
UR - http://eudml.org/doc/280204
ER -