Banach空间的正规结构与对径点

假设S（X）是Banach空间X的单位球面，作引进了四个新的几何参数：Jε（X）=sup{βε（x），x∈S（X）}，jε（X）=inf{βε（x），x∈S（X）}，Gε（X）=sup{αε（x），x∈S（X）}，gε（X）=inf{αε（x），x∈S（S）}，其中≤ε≤1,βε（x）=sup{min{‖x εy‖，‖x-εy‖，y∈S（X）}}，αε（x）=inf{max{‖x εy‖，‖x-εy‖，y∈S（X）}}，讨论了这些参数的性质，本主要结果是：如果主要结果是：如果有一个ε，0≤ε≤1,使得Jε（X）＜1 ε/2或gε（X）＞1 ε/3,那末X有一至正规结构。

Normal Structure and Antipodal Points in Banach Spaces

Let X be a Banach space and S(X)={x∈X, ‖x‖=1} be the unit sphere of X. Four new parameters Jε(X)=sup{βε(x), x∈S(X)}, jε(X)=inf{βε(x), x∈S(X)}, Gε(X)=sup{αε(x),x∈S(X)}, and gε(X)=inf{αε(x),x∈S(X)} where βε(x)=sup{min{‖x+εy‖, ‖x-εy‖, y∈S(X)}}, and αε(x)=inf{max{‖x+εy‖, ‖x-εy‖, y∈S(X)}} 0ε1 and x∈S(X), are introduced and studied. The main result is that a Banach space X with Jε(X)＜1+(ε)/(2), or gε(X)＞1+(ε)/(3) for some 0ε1 has uniform normal structure.