全函数空间和置换空间的一些性质

In this paper, an equivalent relation among the reflexivity, weak sequential completeness and bounded completeness in full function space is given. Some results on weakly sequential compactness of subset and the property （u） in substitution spaces are obtained.     

关于有界闭凸集上的滴和弱滴性质

本文证明了Banach空间中有界闭凸集有滴和弱滴性质的三个等价条件及Banach空间与其共轭空间有滴和弱滴性质的四个等价条件.     

On k-Strictly Convex and k-Very Smooth Banach Spaces

Ｏｎｋ－ＳｔｒｉｃｔｌｙＣｏｎｖｅｘａｎｄｋ－ＶｅｒｙＳｍｏｏｔｈＢａｎａｃｈＳｐａｃｅｓＺｈａｎｇＺｉｈｏｕ（张子厚）（ＨｕａｉｎａｎＴｅｌｅｃｉｓｉｏｎＵｎｉｖｅｒｓｉｔｙ,Ｈｕａｉｎａｎ,Ａｎｈｕｉ,２３２００１）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓ...     

On the Weak＊ Drop Property for Polar of Closed Bounded Convex Sets

We define and study the weak* drop property for the polar of a closed bounded convex set in a Banach space which is both a generalization of the weak* drop property for dual norm in a Banach space and a characterization of the sub-differentialmapping x→эp(x) from S(X) into 2^S(X*) that is norm upper semi-continuous and norm compact-valued.     

A note in approximative compactness and midpoint locally k-uniform rotundity in Banach spaces

In this article, we prove the following results: (1) A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; (2) A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set.     

On very rotund banach space

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ [1 ] ,Ｆ .Ｓｕｌｌｉｖａｎｄｅｆｉｎｅｄｔｈｅｖｅｒｙｒｏｔｕｎｄｓｐａｃｅ ,ｗｈｉｃｈｉｓｔｈｅｄｕａｌｎｏｔｉｏｎｏｆｖｅｒｙｓｍｏｏｔｈｓｐａｃｅ.Ｉｎ [2 ] ,ｔｈｅｗｅａｋｌｙｅｘｐｏｓｅｄｐｏｉｎｔｗａｓｉｎｔｒｏｄｕｃｅｄ ,ｗｈｉｃｈｉｓａｇｅｎｅｒａｌｉｚａｔｉｏｎｏｆｔｈｅｓｔｒｏｎｇｌｙｅｘｐｏｓｅｄｐｏｉｎｔ.Ｉｔｉｓｋｎｏｗｎｔｈａｔｔｈｅｒｅｉｓａｃｌｏｓｅｄｃｏｎｎｅｃｔｉｏｎｂｅｔｗｅｅｎｔｈｅｓｔｒｏｎｇｌｙｅｘｐｏｓｅｄｐｏｉｎｔｓａｎｄ…     

关于β范空间中单位球面间线性等距扩张的一个注记

In this paper, we give four general results on linear extension of isometries between the unit spheres in β-normed spaces. These results improve the corresponding theorems in β-normed spaces.     

关于非常圆的Banach空间

证明了非常圆空间的3个特征。讨论了非常圆空间和Banach空间几何性质之间的关系。建立了弱暴露点和Radon-Nikodym性质之间的联系。