The Weak Drop Property on Closed Convex Sets


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 ∈ A such That co({x} ∪ C) ∩ A = {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 Mathematics subject classification (Amer. Math. Soc.): 46B20,46B10. © 1994, Australian Mathematical Society. All rights reserved.

Publication Title

journal of The Australian Mathematical Society