Banach空间的亚凸性

The quasi-convexity in Banach space

本文引进亚一致凸、弱亚一致凸、亚局部一致凸、弱亚局部一致凸的Banach空间,它们分别是一致凸,弱一致凸,局部一致凸,弱局部一致凸概念的推广.我们分别得到了一致凸、弱一致凸、局部一致凸、弱局部一致凸的几个等价条件,证明了亚一致凸,弱亚一致凸、亚局部一致凸、弱亚局部一致凸空间的一些性质,并分别给出了亚一致凸、弱亚一致凸、亚局部一致凸、弱亚局部一致凸的对偶概念.

In this paper, We introduce the quasi-uniformly convex, weakly quasi uniformly convex,quasi-locally uniformly convex and weakly quasi-locally uniformly convex Banach space. They are respe ctively a generalization of the uniformly convexity, weakly uniformly con-vesity, locally uniformly convexity and weakly locally uniformly convexity. We obtain some e-quivalent conditions of the uniformly convex, weakly uniformly convex, locally uniformly convex and weakly locally uniformly convex Banach space respectively,and prove some properties of the quasi-uniformly convex space,weakly quasi-uniformly convex space,quasi-locally u-niformly convex space and weakly quasi-locally uniformly convex space. We also give the dual notion of quasi-uniformly conveity ,weakly quasi-uniformly convexity,quasi-locally uniformly convexity and weakly quasi-locally uniformly convexity respectively.