Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 13 (2006), No. 3, 711--719Copyright Heldermann Verlag 2006 Weak-Star Convergence of Convex Sets Simon P. Fitzpatrick Adrian S. Lewis ORIE, Cornell University, Ithaca, NY 14853, U. S. A. aslewis@orie.cornell.edu [Abstract-pdf] We show that if a Banach space $X$ is weakly compactly generated and $C$, $C_n$ are weak-star-closed 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 weak-star limit $C$. Keywords: Scalar convergence, weak-star convergence, set convergence, weakly compactly generated. [ Fulltext-pdf  (271  KB)] for subscribers only.