Geodesic
Weak-Star Convergence of Convex Sets
Journal of convex analysis, Tome 13 (2006) no. 3, pp. 711-719.

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

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 $C$.
Mots-clés : Scalar convergence, weak-star convergence, set convergence, weakly compactly generated 
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     author = {S. P. Fitzpatrick and A. S. Lewis},
     title = {Weak-Star {Convergence} of {Convex} {Sets}},
     journal = {Journal of convex analysis},
     pages = {711--719},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {2006},
     url = {http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a13/}
}
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S. P. Fitzpatrick; A. S. Lewis. Weak-Star Convergence of Convex Sets. Journal of convex analysis, Tome 13 (2006) no. 3, pp. 711-719. http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a13/