赋Φ-Amemiya范数的Orlicz空间包含序渐进等距c0复本

doi:10.3969/j.issn.1000-5641.201911007

华东师范大学学报（自然科学版） ›› 2020, Vol. 2020 ›› Issue (2): 35-40.doi: 10.3969/j.issn.1000-5641.201911007

赋Φ-Amemiya范数的Orlicz空间包含序渐进等距c₀复本

崔云安, 安莉丽

哈尔滨理工大学理学院, 哈尔滨　150080

收稿日期:2019-01-24 发布日期:2020-03-16
作者简介:崔云安,男,教授.研究方向为泛函分析.E-mail:cuiya@hrbust.edu.cn;安莉丽,女,硕士研究生.研究方向为泛函分析.E-mail:1468126191@qq.com
基金资助:
国家自然科学基金（11871181，11701125）

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

CUI Yun'an, AN Lili

College of Science, Harbin University of Science and Technology, Harbin　150080, China

Received:2019-01-24 Published:2020-03-16

摘要/Abstract

摘要： 在Orlicz空间中, 我们引进了一个与Luxemburg范数等价的新范数—赋Φ-Amemiya范数: ${\left\| x \right\|_{\Phi ,{\Phi _1}}} = \inf \left\{ {\frac{1}{k}\left( {1 + \Phi \left( {{{ I}_{{\Phi _1}}}\left( {kx} \right)} \right)} \right)} \right\}$. 并证明了由此范数构成的Orlicz函数空间$\left\{ {{L_{\Phi ,{\Phi _{\rm{1}}}}},{{\left\| \cdot \right\|}_{\Phi ,{\Phi _1}}}} \right\}$是Banach空间. 据此得到了赋Φ-Amemiya范数的Orlicz空间包含序渐近等距c₀复本的条件.

关键词: Orlicz空间, Amemiya范数, Δ₂条件, c₀的序渐近等距复本

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

中图分类号:

O177.3

崔云安, 安莉丽. 赋Φ-Amemiya范数的Orlicz空间包含序渐进等距c₀复本[J]. 华东师范大学学报（自然科学版）, 2020, 2020(2): 35-40.

CUI Yun'an, AN Lili. The Orlicz space equipped with the Φ-Amemiya norm contains an order asymptotically isometric copy of c₀[J]. Journal of East China Normal University(Natural Science), 2020, 2020(2): 35-40.

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赋Φ-Amemiya范数的Orlicz空间包含序渐进等距c₀复本

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

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