局部凸空间中若干种k-凸性和k-光滑性的研究  

Study on Some Kinds of k-Convexity and k-Smoothness in Locally Convex Spaces

作　　者：郝建军[1] 刘德[1] 

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《内蒙古大学学报（自然科学版）》2010年第1期34-40,共7页Journal of Inner Mongolia University：Natural Science Edition

摘　　要：利用k维凸体体积统一给出了局部凸空间中k-一致凸和k-一致光滑,k-局部一致凸和k-局部一致光滑等定义,证明了它们是赋范空间相应概念的推广,并指出了它们之间的蕴含关系以及在P-自反意义下的对偶关系.The definitions of k-uniformly convex, locally k-uniformly convex, k-uniformly smooth,locally k-uniformly smooth, etc. in locally convex spaces are given by k-dimension convex volume. It is proved that they are the extension of corresponding concepts in normed spaces. Their deduce and dual relationship are also discussed in the case of P-reflexivity.

关 键 词：局部凸空间 k-凸性 K-光滑性 P-自反 对偶 

分 类 号：O177.2[理学—数学] O177.31[理学—基础数学]