Local rotundity structure of Cesàro–Orlicz sequence spaces

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• 作者：Paweł ; Foralewski ; Henryk Hudzik ; Alicja Szymaszkiewicz
• 关键词：Orlicz function ; Orlicz sequence space ; Cesà ; ro– ; Orlicz sequence space ; Extreme point ; Strong U-point ; Best approximation
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2008
• 出版时间：1 September 2008
• 年：2008
• 卷：345
• 期：1
• 页码：410-419
• 全文大小：213 K

文摘

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 c₀ 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.