Orlicz空间的k-端点和k-强端点

k-Extreme Points and k-Strongly Extreme Points in Orlicz Spaces

证明了Banach空间单位球面上的k-端点(k-强端点)必为(k+1)—端点((k+1)—强端点),给出了赋Luxemburg范数的Orlicz空间单位球k—端点(k—强端点)的判据,并据此得到了赋Luxemburg范数Orlicz空间是K严格凸和中点局部K一致凸的条件。

In this paper, we prove that a k-extreme point(k-strongly extreme point) of the unit sphere in Banach spaces must be a(k+1)-extreme point((k+1)-strongly extreme point). Criteria for k-extreme points and k-strongly extreme points of the unit ball in Orlicz spaces with Luxemburg norm is given. And by it we obtain sufficient and necessary conditions for the Orlicz spaces with Luxemburg norm to be and.