Journal of Convex Analysis 20 (2013), No. 2, 495--500
Copyright Heldermann Verlag 2013
Normal Cones and Continuity of Vector-Valued Convex Functions
Andrea Carioli
Via L. da Vinci 31/A, 20030 Senago (MI), Italy
andrea.carioli@studenti.unimi.it
Libor Vesely
Dip. di Matematica, Università degli Studi, Via C. Saldini 50, 20133 Milano, Italy
libor.vesely@unimi.it
It is known that convex functions with values in an ordered Banach space Y, whose positive cone Y+ is normal, have the same continuity properties as real-valued convex functions. We show that normality of Y+ is not only sufficient, but also necessary for this.
Keywords: Convex operator, vector-valued convex function, ordered normal linear space, normal cone.
MSC: 47H99; 46B40
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