Geodesic
The Exact Value of Normal Structure Coefficients and WCS coefficients in a Class of Orlicz Function Spaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 4, pp. 89-92.

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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 $1$ (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
Mots-clés : WCS coefficient, normal structure coefficient. 
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     title = {The {Exact} {Value} of {Normal} {Structure} {Coefficients} and {WCS} coefficients in a {Class} of {Orlicz} {Function} {Spaces}},
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Ya. Q. Yan. The Exact Value of Normal Structure Coefficients and WCS coefficients in a Class of Orlicz Function Spaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 4, pp. 89-92. http://geodesic.mathdoc.fr/item/FAA_2005_39_4_a10/

[1] Brodskii M. S., Milman D. P., Dokl. AN SSSR, 59 (1948), 837–840 | MR | Zbl

[2] Bynum W., Pacific J. Math., 86 (1980), 619–624 | DOI | MR

[3] Dominguez Benavides T., Rodriguez R. J., Nonlinear Anal., 20 (1993), 349–358 | DOI | MR | Zbl

[4] Rao M. M., Ren Z. D., Applications of Orlicz spaces, Marcel Dekker, New York, 2002, 73–116 | MR

[5] Yan Y. Q., Studia Math., 147:1 (2001), 73–88 | DOI | MR | Zbl

[6] Yan Y. Q., Southeast Asian Bull. Math., 25 (2002), 769–782 | DOI | MR | Zbl