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Brief communications
The Exact Value of Normal Structure Coefficients and WCS coefficients in a Class of Orlicz Function Spaces
Ya. Q. Yan Soochow University
Abstract:
Let $\Phi$ be an $N$-function. Then the normal structure coefficients $N$ and the weakly convergent sequence coefficients $WCS$ of the Orlicz function spaces $L^\Phi[0,1]$ generated by $\Phi$ and equipped with the Luxemburg and Orlicz norms have the following exact values. (i) If $F_\Phi(t)=t\varphi(t)/\Phi(t)$ is decreasing and $1<C_\Phi<2$ (where $C_\Phi=\lim_{t\to+\infty}t\varphi(t)/\Phi(t)$), then
$$
N(L^{(\Phi)}[0,1])=N(L^{\Phi}[0,1])=WCS(L^{(\Phi)}[0,1])=WCS(L^{\Phi}[0,1])=2^{1-1/C_\Phi}.
$$
(ii) If $F_\Phi(t)$ is increasing and $C_\Phi>2$, then
$$
N(L^{(\Phi)}[0,1])=N(L^{\Phi}[0,1])=WCS(L^{(\Phi)}[0,1])=WCS(L^{\Phi}[0,1])=2^{1/C_\Phi}.
$$
Keywords:
Orlicz space, WCS coefficient, normal structure coefficient.
Received: 05.03.2004
Citation:
Ya. Q. Yan, “The Exact Value of Normal Structure Coefficients and WCS coefficients in a Class of Orlicz Function Spaces”, Funktsional. Anal. i Prilozhen., 39:4 (2005), 89–92; Funct. Anal. Appl., 39:4 (2005), 321–323
Linking options:
https://www.mathnet.ru/eng/faa91https://doi.org/10.4213/faa91 https://www.mathnet.ru/eng/faa/v39/i4/p89
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Abstract page: | 423 | Full-text PDF : | 157 | References: | 31 |
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