Geodesic
Operator Topologies and Graph Convergence
Journal of convex analysis, Tome 16 (2009) no. 3, pp. 687-698

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 47A05, 46A17, 54B20
Mots-clés : Operator topology, polar topology, bornological convergence, Attouch-Wets Convergence, normed linear space, convex set, starshaped set 
@article{JCA_2009_16_3_JCA_2009_16_3_a5,
     author = {G. Beer},
     title = {Operator {Topologies} and {Graph} {Convergence}},
     journal = {Journal of convex analysis},
     pages = {687--698},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2009},
     url = {http://geodesic.mathdoc.fr/item/JCA_2009_16_3_JCA_2009_16_3_a5/}
}
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G. Beer. Operator Topologies and Graph Convergence. Journal of convex analysis, Tome 16 (2009) no. 3, pp. 687-698. http://geodesic.mathdoc.fr/item/JCA_2009_16_3_JCA_2009_16_3_a5/