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

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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