
Journal of Convex Analysis 17 (2010), No. 1, 159171 Copyright Heldermann Verlag 2010 On the Lower Bounds of Kottman Constants in Orlicz Function Spaces Z. D. Ren Department of Mathematics, University of California, Riverside, CA 92521, U.S.A. jgiu98@hotmail.com [Abstractpdf] Let $L^{(\Phi)}(\Omega)$ and $L^{\Phi}(\Omega)$ be the Orlicz function spaces defined by an $N$function $\Phi$, equipped with the gauge norm and the Orlicz norm respectively, where $\Omega=[0,1]$ or $[0,\infty)$. The Kottman constants $K(L^{(\Phi)}(\Omega))$ and $K(L^{\Phi}(\Omega))$ were discussed by M. M. Rao and the author in Chapter 5 of their book ``Applications of Orlicz Spaces'' [Marcel Dekker Inc., New York, 2002]. The author obtains some improvments on the lower bounds of these constants in Section 2 (Theorems 1 and 2). Several examples are given in Section 3 which will be used to make comments upon the papers of Y. Q. Yan [On the exact value of packing spheres in a class of Orlicz function spaces, J. Convex Analysis 11(2) (2004) 391400], and J. Han and X. L. Li [Exact value of packing spheres constant in class of Orlicz function spaces (in Chinese), J. Tongji Univ. 30(7) (2002) 895899]. Keywords: Orlicz function space, Kottman constant and packing constant. MSC: 46B30 [ Fulltextpdf (152 KB)] for subscribers only. 