Yan Yaqiang
Riesz angles of Orlicz sequence spaces

Comment.Math.Univ.Carolinae 43,1 (2002) 133-147.

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

Keywords: Orlicz space, $N$-function, index function, Riesz angle
AMS Subject Classification: 46E30