The exact value of normal structure coefficients in a class of Orlicz Sequence spaces

Abstract

Main results: The normal structure coefficients of the Orlicz Sequence spacesl ^Ф generated by theN-function Φ equipped with Luxemburg and Orlicz norm have the exact value:

• (i) IfF _Ф(t)=tϕ(t)/Φ(t) is decreasing,C ⁰_Ф >2, then$N(l^{(\Phi )} ) = N(l^\Phi ) = 2^{C_\Phi ^{\mathop 0\limits^{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{1} } } }$;

• (ii) IfF _qФ(t) is increasing, 1<C ⁰_Ф <2, then$N(l^{(\Phi )} ) = N(l^\Phi ) = 2^{^{1 - } C_\Phi ^{\mathop 0\limits^{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{1} } } }$, where$C_\Phi ^0 = \mathop {\lim }\limits_{t \to 0} F_\Phi (t)$.