局部凸空间的P-自反性和某些凸性光滑性之间的对偶特征(Ⅰ)(英文)  

P-reflexivity and Dual Characterizations between Some Convexity and Smoothness of Locally Convex Spaces(Ⅰ)

作　　者：于亚璇[1,2] 刘德[1] 罗成[1] 

机构地区：[1]内蒙古大学理工学院数学系 [2]大连理工大学应用数学系,大连116024

出　　处：《内蒙古大学学报（自然科学版）》2007年第2期138-144,共7页Journal of Inner Mongolia University：Natural Science Edition

基　　金：内蒙古自然科学基金资助项目(200308020101)~~

摘　　要：设X是实线性空间,P是X上的一族分离半范数且TP是X上由P生成的局部凸分离拓扑.引入半范数族P的S-最简形式和P-自反局部凸空间(X,TP)的概念,证明了半范数族P和它的每一个S-最简形式都生成X上相同的局部凸拓扑.此外,讨论了P-自反性和自反性之间的关系.还指出当X是赋范线性空间时,P-自反性和自反性是两个等价概念.Let X be a real linear space,P a family of separated seminorms on X and Tp the locally convex separated topology on X generated by P. The concepts of the S-simplest form of a seminorm family P and the P-reflexive locally convex space （X,Tp） are introduced. The seminorm family P and its every S-simplest form generate the same locally convex separated topology on X are proved. Moreover ,the relations between the P-reflexivity and the reflexivity are discussed. It is shown that the P-reflexivity and the reflexivity are two equivalent concepts when X is a normed linear space.

关 键 词：局部凸空间 S-最简半范数族 P-自反空间 偶对 凸性 光滑性 

分 类 号：O189.11[理学—数学]