Banach空间凸性光滑性的进一步探讨(Ⅱ)──各类凸性空间的等价性  

Further Exploration on Convexity and Smoothness of Banach Spaces──Equivalence of the Various Kinds of Convexity Spaces

作　　者：郝飞[1] 刘德[1] 罗成[1] 

机构地区：[1]内蒙古大学数学系,内蒙古呼和浩特010021

出　　处：《内蒙古大学学报（自然科学版）》2002年第2期125-129,共5页Journal of Inner Mongolia University：Natural Science Edition

基　　金：内蒙古自然科学基金资助项目 (批准号:990 30 1 -1 )

摘　　要：引入和极光滑 (非常极光滑或一致极光滑 )空间对偶的极凸 (非常极凸或一致极凸 )空间 ,讨论了它们的性质及其和已知凸性空间的联系 ,给出各种凸性的一系列等价条件 .The extremely convex (very extremely convex and uniformly extremely convex) spaces,which are the spaces dualized with the extremely smooth (very extremely smooth and uniformly extremely smooth) spaces,are introduced,and their properties and the relations with some known convexity spaces are discussed.Moreover,a series of the equivalent conditions of the various kinds of convexity spaces are given.

关 键 词：凸性空间 对偶关系 BANACH空间 凸性 光滑性 等价性 极凸空间 极光滑空间 

分 类 号：O177.2[理学—数学]