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Local rotundity structure of Cesàro--Orlicz sequence spaces. (English) Zbl 1155.46007
Summary: 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 a strong U-point is essentially stronger than the notion of an 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 an SU-point, that is, the notion of an extreme point is not strong enough here.

46B20Geometry and structure of normed linear spaces
46B45Banach sequence spaces
Full Text: DOI
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