U_β-凸模和正规结构

Modulus of U_β-Convexity and Normal Structure

本文给出了uβ-凸模,和Uβ-空间的定义,证明了对于Banach空间X,若uβ(1)>0,则X是一致非方的;若存在δ>0,使uβ(12-)δ>0,则X具有正规结构.

In this paper, we mainly define modulus of uβ- convexity and Uβ- space. We prove that if uβ（1）〉0 , then X is 1 uniformly nonsquare. We also prove that if there exists a δ〉0 such that uβ（（1）/（2）-δ）〉0, then X has normal structure.