摘要
本文研究了k非常极凸和k非常极光滑空间的问题.利用Banach空间理论的方法,证明了k非常极凸空间和k非常极光滑空间是一对对偶概念,并且k非常极凸空间(k非常极光滑空间)是严格介于k一致极凸空间和k非常凸空间(k一致极光滑空间和k非常光滑空间)之间的一类新的Banach空间,得到了k非常极凸空间和k非常极光滑空间的若干等价刻画以及k非常极凸(k非常极光滑性)与其它凸性(光滑性)之间的蕴涵关系,推广了非常极凸空间和非常极光滑空间,完善了k非常极凸空间及其对偶空间的研究.
In this article, we study the problems of about k-very extreme convex spaces and k-very extreme smooth spaces. Using the method of Banach spaces theory, we show that the k-very extreme convex space is just the duality of k-very extreme smooth space and lies strictly between k-uniformly extreme convex spaces and k-very convex spaces. We obtain some characteristic descriptions of k-very extreme convex spaces or k-very extreme smooth space, and study the relation between k-very extreme convexity （resp. k-very extreme smoothness） with various convexity （resp. various smoothness）. The results generalize the very extreme convexity and very extreme smoothness, and perfect the research on k-very extreme convex space and its dual space.
出处
《数学杂志》
CSCD
北大核心
2011年第6期1109-1116,共8页
Journal of Mathematics
基金
国家自然科学基金(11061022)资助
关键词
k非常极凸
k非常极光滑
k非常凸
k一致极凸
k-very extreme convex space
k-very extreme smooth space
k-very convex space
k-uniformly extreme convex space
