正规六边形和更广泛具有正规结构的Banach 空间

假设Ｘ是一个实Ｂａｎａｃｈ空间,Ｓ（Ｘ）是单位球面。作者引进了一个新的几何参数（Ｈ（Ｘ）,讨论了Ｈ（Ｘ）和Ｎｅｕｍａｎｎ－Ｊｏｒｄａｎ常数ＣＮＪ（Ｘ）Ｒ 性质以及Ｈ（Ｘ）和其他几何常数的关系,本文主要结果是：Ｈ（Ｘ）〈２或ＣＮＪ（Ｘ）〈４／５一致正规结构。

NORMAL HEXAGON AND MORE GENERAL BANACH SPACES WITH UNIFORM NORMAL STRUCTURE

Let X be a Banach space, S(X) be the unit sphere of X. A geometric parameter H(X) =Sup{‖x+y‖∧‖2x-y‖, for any x,y, and x-y∈S(X)} is introduced; the properties of H(X) and Neumann-Jordan constant CNJ(X),and the relationship between H(X) and other geometric concepts are discussed. The main result is that either H(X)＜2, or CNJ(X)＜4/5 implies normal structure.