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.
出处
《内蒙古大学学报（自然科学版）》
CAS
CSCD
北大核心
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)~~
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
locally convex space iS-simplest seminorm family
P-reflexive space dual pair
convexity
smoothness
