Some remarks of drop property
Abstract
Let C be a proper closed convex set. C is said to have the drop property if for any nonempty closed set A disjoint with C, there is a ∈ A such that co(a, C) ⋂ A = (a). We show that if X contains a noncompact set with the drop property, then X is reflexive. Moreover, we prove that if C is a noncompact closed convex subset of a reflexive Banach space, then C has the drop property if and only if C satisfies the following conditions: (i) the interior of C is nonempty; (ii) C does not have any asymptote, and the boundary of C does not contain any ray; and (iii) every support point x of C is a point of continuity. © 1992 American Mathematical Society.
Publication Title
Proceedings of the American Mathematical Society
Recommended Citation
Lin, P. (1992). Some remarks of drop property. Proceedings of the American Mathematical Society, 115 (2), 441-446. https://doi.org/10.1090/S0002-9939-1992-1095224-2
