Local rotundity structure of generalized Orlicz–Lorentz sequence spaces

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).