
Journal of Convex Analysis 21 (2014), No. 3, 663680 Copyright Heldermann Verlag 2014 Order Asymptotically Isometric Copies of c_{o} in the Subspaces of Order Continuous Elements in Orlicz Spaces Yunan Cui Dept. of Mathematics, Harbin University of Science and Technology, Harbin 150080, PR China cuiya@hrbust.edu.cn Henryk Hudzik Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61614 Poznan, Poland hudzik@amu.edu.pl Grzegorz Lewicki Dept. of Mathematics, Jagiellonian University, Lojasiewicza 6, 30348 Krakow, Poland Grzegorz.Lewicki@im.uj.edu.pl [Abstractpdf] 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 AmemiyaOrlicz norm. In case of a nonatomic, complete and $\sigma$finite measure space $(T,\Sigma,\mu)$ and the Luxemburg norm (the AmemiyaOrlicz 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 nonsquare space). In both cases, the Luxemburg and the AmemiyaOrlicz 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 nontrivial. The asymptotically isometric copies of $c_0$ that are built in our theorems are order copies. Keywords: Orlicz space, subspace of order continuous elements, Luxemburg norm, AmemiyaOrlicznorm, condition Delta2, asymptotically isometric copy of csubo, the fixed point property. MSC: 46B04, 46E30 [ Fulltextpdf (166 KB)] for subscribers only. 