Convex transformations with Banach lattice range.

• Autores: Roman Ger
• Localización: Stochastica: revista de matemática pura y aplicada, ISSN 0210-7821, Vol. 11, Nº. 1, 1987, págs. 13-23
• Idioma: inglés
• Títulos paralelos:
  • Transformaciones convexas con estructura enrejada de Banach.
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• Resumen

  • 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.