Riesz angles of Orlicz sequence spaces

Yan, Ya Qiang

Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 1, pp. 133-147.

Résumé

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 $\max (2\beta^0_{\Psi}, 2\beta '_{\Psi})\leq a(l^{\Phi}) \leq\frac{2}{\theta^0_{\Phi}}$.

Détail

Classification : 46B45, 46E30
Keywords: Orlicz space; $N$-function; index function; Riesz angle