Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 21 (2014), No. 3, 663--680Copyright Heldermann Verlag 2014 Order Asymptotically Isometric Copies of co 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, 61-614 Poznan, Poland hudzik@amu.edu.pl Grzegorz Lewicki Dept. of Mathematics, Jagiellonian University, Lojasiewicza 6, 30-348 Krakow, Poland Grzegorz.Lewicki@im.uj.edu.pl [Abstract-pdf] 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. Keywords: 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. MSC: 46B04, 46E30 [ Fulltext-pdf  (166  KB)] for subscribers only.