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 
@article{JCA_2006_13_3_JCA_2006_13_3_a13,
     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/}
}
TY  - JOUR
AU  - S. P. Fitzpatrick
AU  - A. S. Lewis
TI  - Weak-Star Convergence of Convex Sets
JO  - Journal of convex analysis
PY  - 2006
SP  - 711
EP  - 719
VL  - 13
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a13/
ID  - JCA_2006_13_3_JCA_2006_13_3_a13
ER  - 
%0 Journal Article
%A S. P. Fitzpatrick
%A A. S. Lewis
%T Weak-Star Convergence of Convex Sets
%J Journal of convex analysis
%D 2006
%P 711-719
%V 13
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a13/
%F JCA_2006_13_3_JCA_2006_13_3_a13
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/