广西科学

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王翠玲,魏文展,周玲丽.k-接近一致光滑Bananch空间[J].广西科学,2006,13(4):267-270. [点击复制]
WANG Cui-ling,WEI Wen-zhan,ZHOU Ling-li.k-Nearly Uniformly Smooth Banach Spaces[J].Guangxi Sciences,2006,13(4):267-270. [点击复制]

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k-接近一致光滑Bananch空间
王翠玲¹, 魏文展², 周玲丽³
0 字体:加大+\|默认\|缩小-
(1.集美大学理学院, 福建厦门 361021;2.广西经贸职业技术学院, 广西南宁 530021;3.山东交通学院, 山东济南 250023)

摘要:

定义k-接近一致光滑模,利用其给出k-接近一致光滑(k-NUS)空间的概念,证明k-接近一致光滑空间与k-接近一致凸空间是对偶概念,同时引入具有w_k^*性质的空间,给出k-接近一致光滑空间的一个特征刻画,并讨论(k+1)-接近一致光滑空间与接近一致光滑和k-一致光滑(kUS)空间的关系.

关键词: Banach空间接近一致光滑空间 w_k^*性质

DOI：

投稿时间：2006-05-25

基金项目:广西科学基金(0448036);广西教育厅科研项目(2004年)联合资助

k-Nearly Uniformly Smooth Banach Spaces

WANG Cui-ling¹, WEI Wen-zhan², ZHOU Ling-li³

(1.School of Sciences, Jimei University, Xiamen, Fujian, 361021, China;2.Guangxi Economic Trade Polytechnic, Nanning, Guangxi, 530021, China;3.Shandong Jiaotong University, Ji'nan, Shandong, 250023, China)

Abstract:

In this paper,the notion of k-nearly uniformly smooth Banach spaces is introduced,which is a generalization of nearly uniformly smooth Banach spaces,and it is proved that k-nearly uniformly smooth spaces and k-nearly uniformly convex spaces are the dual notions;every k-nearly uniformly smooth spaces is reflexive;one characterization of k-nearly uniformly smooth Banach spaces is given;finally,it is proved that k-uniformly smooth spaces imply(k+1)-nearly uniformly smooth spaces,but its converse is not necessarily true.

Key words: Banach spaces nearly uniformly smooth spaces w_k^* property

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