Hardy-Littlewood-Pólya relation in the best dominated approximation in symmetric spaces

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• 作者：Maciej Ciesielski ^{maciej.ciesielski@put.poznan.pl}
• 关键词：46E30 ; 46B20 ; 46B28
• 刊名：Journal of Approximation Theory
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：213
• 期：Complete
• 页码：78-91
• 全文大小：270 K
• 卷排序：213

文摘

We investigate a correspondence between strict KK-monotonicity, KK-order continuity and the best dominated approximation problems with respect to the Hardy–Littlewood–Pólya relation ≺≺. Namely, we study, in terms of an LKM point and a UKM point, a necessary condition for uniqueness of the best dominated approximation under the relation ≺≺ in a symmetric space EE. Next, we characterize a relation between a point of KK-order continuity and an existence of a best dominated approximant with respect to ≺≺. Finally, we present a compete criteria, written in a notion of KK-order continuity, under which a closed and KK-bounded above subset of a symmetric space EE is proximinal.