[1]韩瑞珠.凸性模与一致非方空间的几个等价条件[J].东南大学学报(自然科学版),1988,18(5):1-7.[doi:10.3969/j.issn.1001-0505.1988.05.001]
 Han Ruizhu (Department of Mathematics and Mechanics).The Modulus of Convexity and the Equivalent Conditions of Uniformly Non-square Spaces[J].Journal of Southeast University (Natural Science Edition),1988,18(5):1-7.[doi:10.3969/j.issn.1001-0505.1988.05.001]
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凸性模与一致非方空间的几个等价条件()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
18
期数:
1988年第5期
页码:
1-7
栏目:
本刊信息
出版日期:
1988-09-20

文章信息/Info

Title:
The Modulus of Convexity and the Equivalent Conditions of Uniformly Non-square Spaces
作者:
韩瑞珠
南京工学院数学力学系
Author(s):
Han Ruizhu (Department of Mathematics and Mechanics)
关键词:
凸性模 一致非方空间 超自反空间
Keywords:
modulus of convexity uniformly non-square space super-reflexive space
分类号:
+
DOI:
10.3969/j.issn.1001-0505.1988.05.001
摘要:
本文证明Banach空间专一致非方的充要条件“存在η_0∈(0,2),使得P(η_0)>0”。从而得Bana■h空间是超自反的充要条件:存在等价范数■·■和η_0∈(0,2),使得P_(u·u(η_0)>0。利用上述结果,本文给出:l^P(X_i)一致非方的充要条件;X一致非方的充要条件;有限维一致非方空间的几何特征。
Abstract:
This paper shows that X is uniformly non-square if P(η_0)>0 for some η_0∈(0, 2). Thus X is super-reflexive iff X exists an equivalent norm which meets the above condition. By virtue of the before mentioned result, the author derives the necessary and sufficient conditions for X and l^p(X_i) being uniformly non-square respectively, and gives a characterization of finitedimensional spaces which are uniformly non-square.
更新日期/Last Update: 2013-04-30