Geodesic
Riesz angles of Orlicz sequence spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 1, pp. 133-147
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We introduce some practical calculation of the Riesz angles in Orlicz sequence spaces equipped with Luxemburg norm and Orlicz norm. For an $N$-function $\Phi(u)$ whose index function is monotonous, the exact value $a(l^{(\Phi)})$ of the Orlicz sequence space with Luxemburg norm is $a(l^{(\Phi)})=2^{\frac{1}{C^0_{\Phi}}}$ or $a(l^{(\Phi)})=\frac{\Phi^{-1}(1)}{\Phi^{-1}(\frac{1}{2})}$. The Riesz angles of Orlicz space $l^\Phi$ with Orlicz norm has the estimation $\max (2\beta^0_{\Psi}, 2\beta '_{\Psi})\leq a(l^{\Phi}) \leq\frac{2}{\theta^0_{\Phi}}$.
We introduce some practical calculation of the Riesz angles in Orlicz sequence spaces equipped with Luxemburg norm and Orlicz norm. For an $N$-function $\Phi(u)$ whose index function is monotonous, the exact value $a(l^{(\Phi)})$ of the Orlicz sequence space with Luxemburg norm is $a(l^{(\Phi)})=2^{\frac{1}{C^0_{\Phi}}}$ or $a(l^{(\Phi)})=\frac{\Phi^{-1}(1)}{\Phi^{-1}(\frac{1}{2})}$. The Riesz angles of Orlicz space $l^\Phi$ with Orlicz norm has the estimation $\max (2\beta^0_{\Psi}, 2\beta '_{\Psi})\leq a(l^{\Phi}) \leq\frac{2}{\theta^0_{\Phi}}$.
Classification : 46B45, 46E30
Keywords: Orlicz space; $N$-function; index function; Riesz angle 
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     author = {Yan, Ya Qiang},
     title = {Riesz angles of {Orlicz} sequence spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {133--147},
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     url = {http://geodesic.mathdoc.fr/item/CMUC_2002_43_1_a10/}
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Yan, Ya Qiang. Riesz angles of Orlicz sequence spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 1, pp. 133-147. http://geodesic.mathdoc.fr/item/CMUC_2002_43_1_a10/