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The weak drop property on closed convex sets

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  09 April 2009

Pei-Kee Lin  and
Xintai Yu
Pei-Kee Lin
Affiliation:
Memphis State University, Memphis TN 38152, USA
Xintai Yu
Affiliation:
East China Normal University, Shanghai, China
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Abstract

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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.

Keywords

weak drop propertyreflexive spaceweak property (α).

MSC classification

Secondary: 46B20: Geometry and structure of normed linear spaces 46B10: Duality and reflexivity
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

References

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