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WCS Coefficients in Orlicz Sequence Spaces

Authors:

Yan Yaqiang

Institution:

(1) Department of Mathematics, Suzhou University, Suzhou, 215006, P. R. China

Abstract:

We introduce some practical calculation of the weakly convergent sequence coefficients of Orlicz sequence spaces equipped with Luxemburg norm and Orlicz norm. For the N-function phgr

(u) of which the index function is monotonuous, the exact value WCS(l⁽⁾) of Orlicz sequence space l⁽⁾ with Luxemburg norm is available, i.e. WCS(l⁽⁾) = $\frac{\Phi^{-1}(1)}{\Phi^{-1}(\frac{1}{\frac{1}{2}})}$ or $2^{1/C^{0}_{\Phi}};$ WCS(l) of l with Orlicz norm has the exact value $2^{1/C^{0}_{\Phi}};$ or estimation

$\hbox{max}\left\{\frac{2\psi \Psi^{-1}(1)]}{\Phi^{-1} \{ \frac{1}{2} \Phi (2 \psi \Psi^{-1}(1)])\}}, \frac{\Phi^{-1} (B^0_{\Psi} - 1}{\Phi^{-1}(\frac{B^0_\Psi -1)}{2}}\right\} \le WCS (I^{\Phi}) \le \frac{2 \Psi^{-1}(\frac{1}{2})}{\Psi^{-1}(1)}$

Keywords:

Orlicz space N-function index function normal structre weakly convergent sequence coefficient

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