Order asymptotically isometric copies of co in the subspaces of order continuous elements in Orlicz spaces

Bibliographic description

punktacja MEiN [2014 A]: 30

title:	Order asymptotically isometric copies of co in the subspaces of order continuous elements in Orlicz spaces
author:	Cui Yunan, Hudzik Henryk, Lewicki Grzegorz
journal title:	Journal of Convex Analysis
volume:	21
issue:	3
date of publication :	2014
pages:	663-680
ISSN:	0944-6532
eISSN:	2363-6394
language:	English
journal language:	English
abstract in English:	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.
affiliation:	Wydział Matematyki i Informatyki : Instytut Matematyki
type:	journal article
subtype:	academic paper

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