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.
@article{urn:eudml:doc:38975,
title = {Convex transformations with Banach lattice range.},
journal = {Stochastica},
volume = {11},
year = {1987},
pages = {13-23},
zbl = {0675.46012},
mrnumber = {MR0970259},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38975}
}
Ger, Roman. Convex transformations with Banach lattice range.. Stochastica, Tome 11 (1987) pp. 13-23. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38975/