K平空间与K强平空间  

K Even Space and K Strongly Even Space

作　　者：吴红霞[1] 苏雅拉图[2] 

机构地区：[1]集美大学理学院数学系,福建厦门361021 [2]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2010年第4期341-345,共5页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：福建省自然科学基金资助项目(2009J05010);内蒙古自然科学基金资助项目(20080404MS0102);集美大学校科研启动基金

摘　　要：引入K平空间、K强平的Banach空间,证明了K平的Banach空间X的共轭空间X*没有K非常光滑点,而S(X*)的非K光滑点在S(X*)中稠密,刻画了凸性更差的Banach空间的性质.另外,还引入强平模、K强平模的概念,并给出强平模、K强平模的充分必要条件.K even space and K strongly even space are introduced.Some facts that no K very smooth point exist in the conjugated space X＊ of K even Banach space X,and that the non-K-smooth point is dense in S（X＊） are proved,which characterize the property of the Banach space with the worse convexity.In addition,the concepts of strongly even module and of K strongly even module are also proposed,and one sufficient and necessary condition for them is given,respectively,which will provide a base to discuss its convexity quantitatively.

关 键 词：平空间 强平空间 K平空间 K强平空间 强平模 K强平模 

分 类 号：O177.2[理学—数学]