Order Asymptotically Isometric Copies of c_o in the Subspaces of Order Continuous Elements in Orlicz Spaces

Y. Cui ; H. Hudzik ; G. Lewicki

Journal of convex analysis, Tome 21 (2014) no. 3, pp. 663-68.

Résumé

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.

Détail

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