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
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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 
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     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},
     year = {2014},
     volume = {21},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2014_21_3_JCA_2014_21_3_a3/}
}
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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/