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Orlicz型序列空间的暴露性
  • ISSN号:1009-1327
  • 期刊名称:《应用泛函分析学报》
  • 时间:0
  • 分类:O177.3[理学—数学;理学—基础数学]
  • 作者机构:[1]上海大学数学系,上海,200444
  • 相关基金:Project Supported in part by the National Natural Science Foundation of China(10971129); SH(JS0101)
中文摘要:

对赋Luxember范数或Orlicz范数的Orlicz型序列空间,诸如古典的、广义的及参数式的,本文总结、补充、比较列出了暴露点及暴露性的充分必要刻画,并对以往结果中的错误进行了修正,从而在序列空间方面系统地完成了有关暴露性的刻画。

英文摘要:

In this talk, we make a survey for criteria of the exposed points and the exposedness for the sequence spaces of Orlicz type, such as the classical Orlicz spaces, general Orlicz spaces and Musielak-Orlicz spaces, endowed with Luxemburg norm and Orlicz norm respectively. It is well known that explosiveness is basic concept in the geometric theory of Banach spaces. They have numerous application in separation theory and control theory. Criteria for exposed points and strongly exposed points in all classical Orlicz spaces were given in [10-12]. In recent years, Zhao and Cui in [6] discussed the problem in Musielak-Orlicz sequence spaces under some restriction. By counterexamples, we show that the criteria of extreme points in [8] and exposed points in [6] are not true, and we give the criteria for exposed points and strongly exposed points in arbitrary Musielak-Orlicz sequence spaces equipped with Luxemburg norm and Orlicz norm by getting rid of the restriction on Musielak-Orlicz function in [6].

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期刊信息
  • 《应用泛函分析学报》
  • 主管单位:中国核工业集团公司
  • 主办单位:中国原子能科学研究院 中国科学院数学与系统科学研究院
  • 主编:阳名珠
  • 地址:北京市海淀区中关村东路55号思源楼c506
  • 邮编:100190
  • 邮箱:journal@amss.ac.cn
  • 电话:010-82541407
  • 国际标准刊号:ISSN:1009-1327
  • 国内统一刊号:ISSN:11-4016/TL
  • 邮发代号:
  • 获奖情况:
  • 国内外数据库收录:
  • 美国数学评论(网络版),德国数学文摘
  • 被引量:880