Abstract

Let L(Φ)(Ω)L^{(\Phi)}(\Omega) and LΦ(Ω)L^{\Phi}(\Omega) be the Orlicz function spaces defined by an NN-function Φ\Phi, equipped with the gauge norm and the Orlicz norm respectively, where Ω=[0,1]\Omega=[0,1] or [0,∞)[0,\infty). The Kottman constants K(L(Φ)(Ω))K(L^{(\Phi)}(\Omega)) and K(LΦ(Ω))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) 391–400], 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) 895–899].

Author information

Contact details are reproduced from the original publication and may be historical.

Z. D. Ren

Department of Mathematics, University of California, Riverside, CA 92521, U.S.A.

jgiu98@hotmail.com

Keywords

  • Orlicz function space
  • Kottman constant and packing constant

Mathematics Subject Classification

46B30

References

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Suggested citation

Z. D. Ren. “On the Lower Bounds of Kottman Constants in Orlicz Function Spaces.” Journal of Convex Analysis 17 (2010), No. 1, 159–171. https://doi.org/10.68381/jca17012

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Published by Heldermann Verlag, 2010. Rights now held by Banach Press LLC.