赋广义Orlicz范数Orlicz函数空间的局部一致凸性

吉林大学学报(理学版)

赋广义Orlicz范数Orlicz函数空间的局部一致凸性

段丽芬¹, 左明霞², 崔云安²

1. 通化师范学院数学学院, 吉林通化 134002； 2. 哈尔滨理工大学应用科学学院, 哈尔滨 150080

收稿日期:2013-07-15 出版日期:2014-03-26 发布日期:2014-03-20
通讯作者: 段丽芬 E-mail:duanlf@126.com

Locally Uniform Rotundity in Orlicz Function SpacesEquipped with the Generalized Orlicz Norm

DUAN Lifen¹, ZUO Mingxia², CUI Yunan²

1. College of Mathematics, Tonghua Teachers University, Tonghua 134002, Jilin Province, China;2. College of Applied Sciences, Harbin University of Science and Technology, Harbin 150080, China

Received:2013-07-15 Online:2014-03-26 Published:2014-03-20
Contact: DUAN Lifen E-mail:duanlf@126.com

摘要/Abstract

摘要：

利用Banach空间凸性理论研究赋广义Orlicz范数Orlicz函数空间的局部一致凸和弱局部一致凸问题, 得到了Orlicz函数空间关于广义Orlicz范数局部一致凸和弱局部一致凸的条件.

关键词: 广义Orlicz范数, Orlicz函数空间, 局部一致凸, 弱局部一致凸

Abstract:

Using convex theories of Banach spaces, the authors studied locally uniform rotundity and weakly locally uniform rotundity of the Orlicz function spaces equipped with the generalized Orlicz norm and obtained sufficient and necessary conditions so as to make them be locally uniform rotund and weakly locally uniform rotund.

Key words: generalized Orlicz norm, Orlicz function space, locally uniform rotund, weakly locally uniform rotund

中图分类号:

O177.3

段丽芬, 左明霞, 崔云安. 赋广义Orlicz范数Orlicz函数空间的局部一致凸性[J]. 吉林大学学报(理学版), 2014, 52(02): 219-223.

DUAN Lifen, ZUO Mingxia, CUI Yunan. Locally Uniform Rotundity in Orlicz Function SpacesEquipped with the Generalized Orlicz Norm[J]. Journal of Jilin University Science Edition, 2014, 52(02): 219-223.

[1]	程亚焕, 段丽芬, 左明霞. 赋广义Orlicz范数Orlicz序列空间的局部一致凸性[J]. 吉林大学学报(理学版), 2015, 53(02): 224-228.
[2]	王宏志, 段丽芬, 左明霞. 赋广义Orlicz范数Orlicz函数空间的H点[J]. 吉林大学学报(理学版), 2014, 52(06): 1181-1185.
[3]	段丽芬, 许晶, 崔云安. 赋广义Orlicz范数的Orlicz函数空间的一致凸性[J]. J4, 2011, 49(05): 809-813.