Geodesic
Order Asymptotically Isometric Copies of co in the Subspaces of Order Continuous Elements in Orlicz Spaces
Journal of convex analysis, Tome 21 (2014) no. 3, pp. 663-68

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

Necessary and sufficient conditions in order that the subspace of order continuous elements of Orlicz sequence space contain an order asymptotically isometric copy of $c_0$ are given for both, the Luxemburg and the Amemiya-Orlicz norm. In case of a non-atomic, complete and $\sigma-$finite measure space $(T,\Sigma,\mu)$ and the Luxemburg norm (the Amemiya-Orlicz norm) such criteria are obtained under the additional assumption that the space $L^\Phi(T,\Sigma,\mu)$ is a dual space (resp. the space $L^\Phi_A(T,\Sigma,\mu)$ is a dual and non-square space). In both cases, the Luxemburg and the Amemiya-Orlicz norm the criteria are given under the necessary assumption that the spaces $E^\Phi(T,\Sigma,\mu)$ and $E^\Phi_A(T,\Sigma,\mu)$ are non-trivial. The asymptotically isometric copies of $c_0$ that are built in our theorems are order copies.
Classification : 46B04, 46E30
Mots-clés : Orlicz space, subspace of order continuous elements, Luxemburg norm, Amemiya-Orlicz-norm, condition Delta-2, asymptotically isometric copy of c-sub-o, the fixed point property 
@article{JCA_2014_21_3_JCA_2014_21_3_a3,
     author = {Y. Cui and H. Hudzik and G. Lewicki},
     title = {Order {Asymptotically} {Isometric} {Copies} of c\protect\textsubscript{o} in the {Subspaces} of {Order} {Continuous} {Elements} in {Orlicz} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {663--68},
     publisher = {mathdoc},
     volume = {21},
     number = {3},
     year = {2014},
     url = {http://geodesic.mathdoc.fr/item/JCA_2014_21_3_JCA_2014_21_3_a3/}
}
TY  - JOUR
AU  - Y. Cui
AU  - H. Hudzik
AU  - G. Lewicki
TI  - Order Asymptotically Isometric Copies of co in the Subspaces of Order Continuous Elements in Orlicz Spaces
JO  - Journal of convex analysis
PY  - 2014
SP  - 663
EP  - 68
VL  - 21
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JCA_2014_21_3_JCA_2014_21_3_a3/
ID  - JCA_2014_21_3_JCA_2014_21_3_a3
ER  - 
%0 Journal Article
%A Y. Cui
%A H. Hudzik
%A G. Lewicki
%T Order Asymptotically Isometric Copies of co in the Subspaces of Order Continuous Elements in Orlicz Spaces
%J Journal of convex analysis
%D 2014
%P 663-68
%V 21
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JCA_2014_21_3_JCA_2014_21_3_a3/
%F JCA_2014_21_3_JCA_2014_21_3_a3
Y. Cui; H. Hudzik; G. Lewicki. Order Asymptotically Isometric Copies of co in the Subspaces of Order Continuous Elements in Orlicz Spaces. Journal of convex analysis, Tome 21 (2014) no. 3, pp. 663-68. http://geodesic.mathdoc.fr/item/JCA_2014_21_3_JCA_2014_21_3_a3/