GENERALIZATION OF THE ARROW-BARANKIN-BLACKWELL THEOREM IN A DUAL-SPACE SETTING

Authors
SONG W
Citation
W. Song, GENERALIZATION OF THE ARROW-BARANKIN-BLACKWELL THEOREM IN A DUAL-SPACE SETTING, Journal of optimization theory and applications, 95(1), 1997, pp. 225-230
Citations number
21
Categorie Soggetti
Operatione Research & Management Science",Mathematics,"Operatione Research & Management Science
Journal title
Journal of optimization theory and applications → ACNP
ISSN journal
00223239
Volume
95
Issue
1
Year of publication
1997
Pages
225 - 230
Database
ISI
SICI code
0022-3239(1997)95:1<225:GOTATI>2.0.ZU;2-R
Abstract
In this note, we provide general sufficient conditions under which, if F is a compact [resp. w()-compact] subset of the topological dual Y- of a nonreflexive normed space Y partially orderer by a closed conve x pointed cone K, then the set of points in F that can be supported by strictly positive elements in the canonical embedding of Y in Y-* is norm dense [resp. w()-dense] in the efficient [maximal] point set of F. This result gives an affirmative answer to the conjecture proposed by Gallagher (Ref. 19), and also generalizes the results stated in Re f. 19 and some space specific results given in Refs. 17, 18, and 11.