Some results on packing in Orlicz sequence spaces

Volume 147 / 2001

Y. Q. Yan Studia Mathematica 147 (2001), 73-88 MSC: 46E30, 46A45. DOI: 10.4064/sm147-1-6


We present monotonicity theorems for index functions of $N$-fuctions, and obtain formulas for exact values of packing constants. In particular, we show that the Orlicz sequence space $l^{(N)}$ generated by the $N$-function $N(v)=(1+|v|)\mathop {\rm ln}\nolimits (1+|v|)-|v|$ with Luxemburg norm has the Kottman constant $K(l^{(N)})={N^{-1}(1)}/{N^{-1}({1}/{2})}$, which answers M. M. Rao and Z. D. Ren's [8] problem.


  • Y. Q. YanDepartment of Mathematics
    Suzhou University
    Suzhou, Jiangsu, 215006, P.R. China

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