赋p-Amemiya(1≤p≤∞)范数的Orlicz序列空间的端点和严格凸性

J4 ›› 2012, Vol. 50 ›› Issue (05): 902-906.

赋p-Amemiya(1≤p≤∞)范数的Orlicz序列空间的端点和严格凸性

段丽芬¹, 许晶¹, 崔云安^2

1. 通化师范学院数学系, 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:2011-10-28 出版日期:2012-09-26 发布日期:2012-09-29
通讯作者: 段丽芬 E-mail:duanlf@126.com.

Extreme Points and Rotundity in Orlicz Sequence Spaces Equipped with p-Amemiya(1≤p≤∞) Norm

DUAN Lifen¹, XU Jing¹, CUI Yunan²

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

Received:2011-10-28 Online:2012-09-26 Published:2012-09-29
Contact: DUAN Lifen E-mail:duanlf@126.com.

摘要/Abstract

摘要：

利用Banach空间及经典Orlicz空间几何理论, 研究一般Orlicz序列空间的严格凸问题, 得到了由一般Orlicz函数生成的赋p-Amemiya范数的Orlicz序列空间中端点的判据, 并由该判据获得了由一般Orlicz函数生成的Orlicz序列空间关于p-Amemiya范数严格凸的充要条件.

关键词: Orlicz序列空间； p-Amemiya范数；端点；严格凸性

Abstract:

By means of geometries of Banach spaces and Orlicz spaces method, the characterizations over rotundity of the Orlicz sequence spaces were discussed. For the Orlicz sequence spaces generated by an Orlicz function and equipped with p-Amemiya norm, the criteria of extreme points were presented. Based on the criteria, sufficient and necessary conditions were derived to make them rotund.

Key words: Orlicz sequence space, pAmemiya norm, extreme point, rotundity

中图分类号:

O177.3

段丽芬, 许晶, 崔云安. 赋p-Amemiya(1≤p≤∞)范数的Orlicz序列空间的端点和严格凸性[J]. J4, 2012, 50(05): 902-906.

DUAN Li-Fen, HU Jing, CUI Yun-An. Extreme Points and Rotundity in Orlicz Sequence Spaces Equipped with p-Amemiya(1≤p≤∞) Norm[J]. J4, 2012, 50(05): 902-906.