
Journal of Convex Analysis 06 (1999), No. 1, 091114 Copyright Heldermann Verlag 1999 Some Geometric Properties in Orlicz Sequence Spaces Equipped with Orlicz Norm Yunan Cui Dept. of Mathematics, Harbin University of Science and Technology, Xuefu Road 52, 150080 Harbin, P. R. China Henryk Hudzik Faculty of Mathematics and Computer Science, Adam Mickiewicz University, U. Matejki 48/49, 60769 Pozna´n, Poland Marian Nowak Inst. of Mathematics, T. Kotarbinski Pedagogical University, Pl. Slowianski 9, 65069 Zielona Góra, Poland Ryszard Pluciennik Inst. of Mathematics, University of Technology, Piotrowo 3A, 60965 Poznan, Poland It is proved that for any reflexive Banach space X, both X and X* are CLUR if and only if both X and X* have property H. Criteria for rotundity, local uniform rotundity, compact local uniform rotundity and property H in Orlicz sequence spaces equipped with the Orlicz norm are given. Criteria for property H, rotundity and LUR were already known in the literature only for finitely valued Orlicz functions which vanish only at zero and are Nfunctions (i.e. they satisfy conditions (0_{1}) and (infty_{1}). All our criteria except Corollary 2.15 are given for arbitrary Orlicz functions. Criteria for smoothness of l_{Φ}^{0} in Corollary 2.15 are given for any finitely valued Orlicz function satisfying condition (infty_{1}), extending the respective result of Chen, Hudzik and Wisla proved only for Orlicz functions vanishing only at zero. Keywords: Orlicz sequence space, compact local uniform rotundity, property H, smoothness, copy of lsubinfinity. MSC: 46E30; 46E40, 46B20 [ Fulltextpdf (251 KB)] 