# Convex transformations with Banach lattice range.

Stochastica (1987)

- Volume: 11, Issue: 1, page 13-23
- ISSN: 0210-7821

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topGer, Roman. "Convex transformations with Banach lattice range.." Stochastica 11.1 (1987): 13-23. <http://eudml.org/doc/38975>.

@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 -

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