Local rotundity structure of Cesàro-Orlicz sequence spaces |
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Authors: | Pawe? Foralewski Alicja Szymaszkiewicz |
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Institution: | a Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland b Institute of Mathematics, Szczecin University of Technology, Al. Piastów 48/49, 70-310 Szczecin, Poland |
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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 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. |
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Keywords: | Orlicz function Orlicz sequence space Cesà ro-Orlicz sequence space Extreme point Strong U-point Best approximation |
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