%A CUI Yun'an, AN Lili
%T The Orlicz space equipped with the Φ-Amemiya norm contains an order asymptotically isometric copy of *c*_{0}
%0 Journal Article
%D 2020
%J Journal of East China Normal University(Natural Science)
%R 10.3969/j.issn.1000-5641.201911007
%P 35-40
%V 2020
%N 2
%U {https://xblk.ecnu.edu.cn/CN/abstract/article_25712.shtml}
%8
%X In Orlicz space, a new norm that is equivalent to the Luxemburg norm is introduced. It is called the Φ-Amemiya norm: ${\left\| x \right\|_{\Phi ,{\Phi _1}}} = \inf \left\{ {\frac{1}{k}\left( {1 + \Phi \left( {{{ I}_{{\Phi _1}}}\left( {kx} \right)} \right)} \right)} \right\}$. It is shown, furthermore, that the Orlicz function space equipped with this norm $\left\{ {{L_{\Phi ,{\Phi _{\rm{1}}}}},{{\left\| \cdot \right\|}_{\Phi ,{\Phi _1}}}} \right\}$ is a Banach space. Hence, this paper demonstrates the conditions for the Orlicz space with the Φ-Amemiya norm to contain an asymptotically isometric copy of *c*_{0}.