Abstract

Necessary and sufficient conditions in order that the subspace of order continuous elements of Orlicz sequence space contain an order asymptotically isometric copy of c0c_0 are given for both, the Luxemburg and the Amemiya-Orlicz norm. In case of a non-atomic, complete and σ−\sigma-finite measure space (T,Σ,μ)(T,\Sigma,\mu) and the Luxemburg norm (the Amemiya-Orlicz norm) such criteria are obtained under the additional assumption that the space LΦ(T,Σ,μ)L^\Phi(T,\Sigma,\mu) is a dual space (resp. the space LAΦ(T,Σ,μ)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 EΦ(T,Σ,μ)E^\Phi(T,\Sigma,\mu) and EAΦ(T,Σ,μ)E^\Phi_A(T,\Sigma,\mu) are non-trivial. The asymptotically isometric copies of c0c_0 that are built in our theorems are order copies.

Author information

Contact details are reproduced from the original publication and may be historical.

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 Poznań, Poland

hudzik@amu.edu.pl

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

Mathematics Subject Classification

46B04, 46E30

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Suggested citation

Y. Cui, H. Hudzik, G. Lewicki. “Order Asymptotically Isometric Copies of c_o in the Subspaces of Order Continuous Elements in Orlicz Spaces.” Journal of Convex Analysis 21 (2014), No. 3, 663–680. https://doi.org/10.68381/jca21035

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