
Journal of Convex Analysis 13 (2006), No. 3, 711719 Copyright Heldermann Verlag 2006 WeakStar Convergence of Convex Sets Simon P. Fitzpatrick Adrian S. Lewis ORIE, Cornell University, Ithaca, NY 14853, U. S. A. aslewis@orie.cornell.edu [Abstractpdf] We show that if a Banach space $X$ is weakly compactly generated and $C$, $C_n$ are weakstarclosed bounded convex nonempty subsets of the dual space $X^*$, then the support functionals $\delta^*_{C_n}$ converge to $\delta^*_C$ pointwise on $X$ if and only if the sequence $(C_n)$ is uniformly bounded with weakstar limit $C$. Keywords: Scalar convergence, weakstar convergence, set convergence, weakly compactly generated. [ Fulltextpdf (271 KB)] for subscribers only. 