一致非l^(1)4 Banach空间的球覆盖特征

A Characterization of Uniform non-l^(1)4 Banach Space via Ball-coverings

证明了X为Banach空间,如果存在两个常量α,β>0,使得对X的任意4维子空间Y,存在一个Y的球覆盖B,C(B)<c(R4,‖·‖1),r(B)≤β且α是远离原点的,则X为一致非l^(1)4空间.

In this paper,it is proved that if there exists two constantsα,β>0,such that for every four dimensional subspace Y of X,there is a ball-covering B of Y satisfying c(B<c(R4,‖·‖1),B isα-off the origin and r(B)≤β,Banach space X is uniformly non-l^(1)4 space.