Compactly Strongly Convex Property in Orlicz Function Spaces Equipped with the Orlicz Norm

ZUO Ming-xia; ZOU Jin-shuang

doi:10.15938/j.jhust.2015.05.025

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Compactly Strongly Convex Property in Orlicz Function Spaces Equipped with the Orlicz Norm

更新时间：2026-08-31

- Compactly Strongly Convex Property in Orlicz Function Spaces Equipped with the Orlicz Norm
- Vol. 20, Issue 5, Pages: 123-126(2015)
- 作者机构：
  
  哈尔滨理工大学应用科学学院,黑龙江,哈尔滨,150080
- 作者简介：
- 基金信息：
- DOI：10.15938/j.jhust.2015.05.025
  CLC： O177.3
- Published：2015
- 稿件说明：
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ZUO Ming-xia, ZOU Jin-shuang. Compactly Strongly Convex Property in Orlicz Function Spaces Equipped with the Orlicz Norm[J]. 2015, 20(5): 123-126.
DOI：

ZUO Ming-xia, ZOU Jin-shuang. Compactly Strongly Convex Property in Orlicz Function Spaces Equipped with the Orlicz Norm[J]. 2015, 20(5): 123-126. DOI： 10.15938/j.jhust.2015.05.025.

摘要

利用Banach空间几何理论中凸性与光滑性的对偶关系

研究了紧强凸性质在赋Orlicz范数的Orlicz函数空间L0M中的刻画问题。首先

给出了赋Luxemburg范数的Orlicz函数空间LM的子空间EM具有S性质的判别准则。然后在赋Orlicz范数Orlicz函数空间L0M中

给出了紧强凸性质的具体刻画

进而得到了这类空间具有强凸性质的充分必要条件。

Abstract

By the dual relationship of convexity and smoothness in the geometric theory of Banach spaces

the depiction for compactly strongly convex property in Orlicz function spaces LM equipped with the Orlicz norm is in- vestigated. Firstly

the criterion for property S in the subspace EM of Orlicz function spaces LM equipped with the Luxemburg norm is gave. Secondly

the specific characterization for compactly strongly convex property in Orlicz function space LM equipped with the Orlicz norm is presented

and then the necessary and sufficient condition that this kind of space have strongly convex property was obtained.

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Related Author

ZUO Mingxia

XU Zeyu

Related Institution

School of Science, Harbin University of Science and Technology

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