Local rotundity structure of generalized Orlicz–Lorentz sequence spaces

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• 作者：Paweł ; Foralewski ; Henryk Hudzik ; Lucjan Szymaszkiewicz
• 关键词：Orlicz– ; Lorentz space ; Extreme point ; Strong U-point
• 刊名：Nonlinear Analysis
• 出版年：2008
• 期刊代码：43_0362546x
• 类别：mt
• 出版时间：1 May 2008
• 卷：68
• 期：9
• 页码：2709-2718
• 文件大小：250 K

摘要

We give some criteria for extreme points and strong U-points in generalized Orlicz–Lorentz sequence spaces, which were introduced in [P. Foralewski, H. Hudzik, L. Szymaszkiewicz, On some geometric and topological properties of generalized Orlicz–Lorentz sequence spaces, Math. Nachr. (in press)] (cf. [G.G. Lorentz, An inequality for rearrangements, Amer. Math. Monthly 60 (1953) 176–179; M. Nawrocki, The Mackey topology of some F-spaces, Ph.D. Dissertation, Adam Mickiewicz University, Poznań, 1984 (in Polish)]). Some examples show that in these spaces the notion of the strong U-point is essentially stronger than the notion of the extreme point. This paper is related to the results from [A. Kamińska, Extreme points in Orlicz–Lorentz spaces, Arch. Math. 55 (1990) 173–180] (see Remark 1).