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The weak drop property on closed convex sets
Published online by Cambridge University Press: 09 April 2009
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 ∈ 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.
MSC classification
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 56 , Issue 1 , February 1994 , pp. 125 - 130
- Copyright
- Copyright © Australian Mathematical Society 1994