Local rotundity structure of Cesàro–Orlicz sequence spaces

Abstract

Some criteria for extreme points and strong U-points in Cesàro–Orlicz spaces are given. In consequence we find a Cesàro–Orlicz sequence space different from c 0 which has no extreme points. Some examples show that in these spaces the notion of the strong U-point is essentially stronger than the notion of the extreme point. Various examples presented in this paper show that there are some differences between criteria for extreme points and strong U-points in Orlicz spaces and in Cesàro–Orlicz spaces. We also show that the uniqueness of the local best approximation needs the notion of SU-point, that is, the notion of the extreme point is not strong enough here.