
Journal of Convex Analysis 16 (2009), No. 3, 687698 Copyright Heldermann Verlag 2009 Operator Topologies and Graph Convergence Gerald Beer Department of Mathematics, California State University, 5151 State University Drive, Los Angeles, CA 90032, U.S.A. gbeer@cslanet.calstatela.edu Let B(X,Y) be the continuous linear transformations from a normed linear space X to a normed linear space Y. This article presents two general results  one for the norm topology on Y and one for the weak topology on Y  that explain how convergence of sequences in B(X,Y) with respect to a topology of uniform convergence on a prescribed family of norm bounded subsets of X is reflected in the bornological convergence of the associated sequence of graphs with respect to a family of subsets of the Cartesian product X times Y. Keywords: Operator topology, polar topology, bornological convergence, AttouchWets Convergence, normed linear space, convex set, starshaped set. MSC: 47A05; 46A17, 54B20 [ Fulltextpdf (149 KB)] for subscribers only. 