Convex transformations with Banach lattice range.

@article{Ger1987,
abstract = {A closed epigraph theorem for Jensen-convex mappings with values in Banach lattices with a strong unit is established. This allows one to reduce the examination of continuity of vector valued transformations to the case of convex real functionals. In particular, it is shown that a weakly continuous Jensen-convex mapping is continuous. A number of corollaries follow; among them, a characterization of continuous vector-valued convex transformations is given that answers a question raised by Ih-Ching Hau.},
author = {Ger, Roman},
journal = {Stochastica},
keywords = {Espacios de Banach; Funciones convexas; Funciones continuas; closed epigraph theorem; strong unit; Jensen-convex; convex analogue of the Banach closed graph theorem; real linear topological Baire space; Banach lattice with strong unit},
language = {eng},
number = {1},
pages = {13-23},
title = {Convex transformations with Banach lattice range.},
url = {http://eudml.org/doc/38975},
volume = {11},
year = {1987},
}

TY - JOUR
AU - Ger, Roman
TI - Convex transformations with Banach lattice range.
JO - Stochastica
PY - 1987
VL - 11
IS - 1
SP - 13
EP - 23
AB - A closed epigraph theorem for Jensen-convex mappings with values in Banach lattices with a strong unit is established. This allows one to reduce the examination of continuity of vector valued transformations to the case of convex real functionals. In particular, it is shown that a weakly continuous Jensen-convex mapping is continuous. A number of corollaries follow; among them, a characterization of continuous vector-valued convex transformations is given that answers a question raised by Ih-Ching Hau.
LA - eng
KW - Espacios de Banach; Funciones convexas; Funciones continuas; closed epigraph theorem; strong unit; Jensen-convex; convex analogue of the Banach closed graph theorem; real linear topological Baire space; Banach lattice with strong unit
UR - http://eudml.org/doc/38975
ER -