赋广义Orlicz范数的Orlicz序列空间的端点和强端点

Extreme and strongly extreme points in Orlicz sequence spaces equipped with the generalized Orlicz norm

给出了由N-函数生成的赋广义Orlicz范数的Oilicz序列空间中端点和强端点的判据,并据此方便地得到了由N-函数生成的Orlicz序列空间关于广义Orlicz范数严格凸和中点局部一致凸的条件.

For the Orlicz sequence spaces generated by a N-function and equipped with the generalized Orlicz norm, criteria of extreme points and strongly extreme points were presented. Based on the criterias, both sufficient and necessary conditions were derived to make these spaces be convex and mid-point locally uniform convex.