局部凸空间的几种光滑性及其等价条件  

Several Kinds of Smoothness in Locally Convex Spaces and Its Equivalent Condtions

作　　者：陈利国[1] 罗成[2] 

机构地区：[1]内蒙古财经学院统计与数学学院,内蒙古呼和浩特010051 [2]内蒙古大学数学科学学院,内蒙古呼和浩特010021

出　　处：《集宁师专学报》2009年第4期1-5,共5页Journal of Jining Teachers College

基　　金：内蒙古自然科学基金资助(200308020101)

摘　　要：设X是一个实线性空间,P是X上的一可分离的半范数族,(X,TP)表示由P生成的局部凸空间,(X,P)为一个偶对.给出偶对(X,P)为(弱)中点局部一致光滑的概念,讨论了它们与其它光滑性之间的关系,此外,还引入性质(WS)、性质(S)的概念,给出几个光滑性的等价性定理,得到了若干等价性,从而推广了Banach空间相应概念和结果。Let X be a real linear spaces,P a family of separated seminorms on X,(X,T_P) a locally convex space generated by P,a dual(X,P).we give the notions of(weakly) midpoint locally uniformly smooth for dual(X,P),disscuss the relationship between them and other smoothness,the notions of property(WS) and(S) are introduced,several equivalent theorems and property are obtained,corresponding notions and results in Banach space is generalized.

关 键 词：(弱)中点局部一致光滑性 性质(WS) 性质(S) 

分 类 号：O177.3[理学—数学]