J Austral Math Soc Ser A 56 pp125--130, 1994.

The Weak Drop Property on Closed Convex Sets

Pei-Kee Lin and Xintai Yu

Abstract

Recall a closed convex set C is said to have the weak drop property if for every weakly sequentially closed set A disjoint from C there exists x Î A such that co({x} ÈC) ÇA = {x}. Giles and Kutzarova proved that every bounded closed convex set with the weak drop property is weakly compact. In this article, we show that if C is an unbounded closed convex set of X with the weak drop property, then C has nonempty interior and X is a reflexive space.

1991 AMS Subject Classification: 46B20, 46B10

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Authors

Pei-Kee Lin

Memphis State University, Memphis TN 38152, USA.

Xintai Yu

East China Normal University, Shanghai, China.