J. Aust. Math. Soc.  75 (2003), 153-161
Computation of nonsquare constants of Orlicz spaces

Y. Q. Yan
  Department of Mathematics
  Suzhou University
  Suzhou, Jiangsu 215006
  P. R. China
  yanyq@pub.sz.jsinfo.net


Abstract
In this paper, we present the computation of exact value of nonsquare constants for some types of Orlicz sequence and function spaces. Main results: Let $\Phi(u)$ be an   N-function, $\phi (t)$ be the right derivative of $\Phi(u)$, then we have
(i)    if $\phi (t)$ is concave, then $ 1/\alpha'_{\Phi}\leq J(l^{(\Phi)})\leq 1/\tilde{\alpha}_{\Phi}$, $J(L^{(\Phi)}[0,\infty ))= 1/\bar{\alpha}_{\Phi}$;
(ii)   if $\phi (t)$ is convex, then $2\beta'_{\Phi}\leq J(l^{(\Phi)})\leq 2\tilde{\beta}_{\Phi}$ , $J(L^{(\Phi)}[0,\infty ))= 2\bar{\beta}_{\Phi}$ .
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