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(Ⅱ)(英文)  

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

作　　者：于亚璇 刘德 罗成 

机构地区：[1]内蒙古大学理工学院数学系

出　　处：《内蒙古大学学报（自然科学版）》2007年第4期366-372,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.证明了半范数族P和它的每一个S-最简形式具有相同的凸性和光滑性.在P-自反的条件下,得到偶对(X,P)是一致光滑的(一致凸的)当且仅当它的强对偶(X,′P′)是一致凸的(一致光滑的).对其它的凸性和光滑性也有类似结果.Let X be a real linear space,P a family of separated seminorms on A and Te the locally convex separated topology on X generated by P. The convexity and smoothness in the locally convex spaces are studied. It is proved that the seminorm family P and every its S-simplest form have the same convexity and smoothness. Under the condition of P-reflexivity,a dual pair （X,P） is uniformly smooth （uniformly convex） if and only if its strong dual pair （X＇,P＇） is uniformly convex （uniformly smooth）. And similar results for the other convexity and smoothness are obtained.

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]