Journal of East China Normal University(Natural Science) ›› 2020, Vol. 2020 ›› Issue (2): 35-40.doi: 10.3969/j.issn.1000-5641.201911007

• Mathematics • Previous Articles     Next Articles

The Orlicz space equipped with the Φ-Amemiya norm contains an order asymptotically isometric copy of c0

CUI Yun'an, AN Lili   

  1. College of Science, Harbin University of Science and Technology, Harbin 150080, China
  • Received:2019-01-24 Published:2020-03-16

Abstract: 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 c0.

Key words: Orlicz space, Amemiya norm, condition Δ2, order asymptotically isometric copy of c0

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