K-drop凸空间中的性质(英文)

SOME PROPERTIES OF K-DROP CONVEX SPACES

为了阐明何为K 强光滑空间的对偶空间 ,本文定义了K drop凸空间并且讨论了该空间的一些性质。同时借助K 强光滑空间的一个等价定义 ,证明了K drop凸空间与K 强光滑空间是对偶空间。文章最后用单位圆的切片给出了K drop凸空间的一等价命题 ,进而建立了K drop凸空间与drop性之间的关系。

In order to illustrate what is the dual space of K\|strong smoothness, we define K\|drop convex space, and discuss some properties of it. Following an equivalent definition of K\|strong smoothness, we prove that the K\|drop convex space is the dual space of K\|strong smoothness. At last, we establish the relationship between K\|drop convexity and Drop\|property following an equivalent denotation of the former, which is described by the slice of unit sphere.