摘要
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.引入偶对(X,P)具有性质(WM)和性质(WM)*等概念.给出四个凸性(光滑性)等价性定理,证明了性质(WM)和性质(WM)*具有对偶关系,从而推广了Banach空间相应概念和结果.
Let X be a real linear space,P be a family of separated seminorms on X. Let （X,TP） denote the locally convex space generated by P,the dual （X,P） is used to denote the space X that has the topolopy Te generated by the semi-norm family P. The notions of property （WM） and property （WM）^＊ for dual （X, P） are introduced, and four equivalent theorems for convexity （smoothness） are established. It is proved that the property （WM） and property （WM）^＊ have dual relationship ,and the corresponding notions and results in Banach spaces are generalized.
出处
《内蒙古大学学报（自然科学版）》
CAS
CSCD
北大核心
2008年第5期499-502,共4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)
