Journal of Convex Analysis 16 (2009), No. 3, 687--698
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, Attouch-Wets Convergence, normed linear space, convex set, starshaped set.
MSC: 47A05; 46A17, 54B20
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