局部凸空间k-严格凸性与k-光滑性的进一步探讨  

k-Strict Convexity and k-Smoothness in Locally Convex Spaces

作　　者：郝建军[1] 刘德[1] 罗成[1] 

机构地区：[1]内蒙古大学理工学院数学系,呼和浩特010021

出　　处：《内蒙古大学学报（自然科学版）》2008年第2期136-139,共4页Journal of Inner Mongolia University：Natural Science Edition

基　　金：内蒙古自治区科学基金资助项目(批准号:200308020101)

摘　　要：利用k维凸体体积给出了局部凸空间中k-严格凸和k-光滑性的定义,证明了它们是B anach空间和偶对(X,P)相应概念的推广,并指出了它们之间的对偶关系.The definitions of k-strict convexity and k-smoothness in locally convex spaces are given by k-dimension convex volume and it is proved that they are the extension of corresponding concepts in Banach spaces and dual （X,P）. Moreover the dual relationship of the k-strict convexity and k-smoothness is discussed.

关 键 词：局部凸空间 K-严格凸 K-光滑性 对偶 

分 类 号：O177.2[理学—数学] O177.31[理学—基础数学]