Local rotundity structure of generalized Orlicz-Lorentz sequence spaces

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, Poznan, 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. Kaminska, Extreme points in Orlicz-Lorentz spaces, Arch. Math. 55 (1990) 173-180] (see Remark 1). (C) 2007 Elsevier Ltd. All rights reserved.