Orlicz spaces with $s$-norms that are abstract M-spaces

Abstract

Let $\Phi$ be an Orlicz function and $L^{\Phi }(X,\Sigma ,\mu )$ the corresponding Orlicz space on a non-atomic, $\sigma$-finite, complete measure space $(X,\Sigma ,\mu )$. We describe those Orlicz spaces equipped with $s$-norms that are abstract M-spaces. Our study generalizes and unifies the results that have been obtained for the Orlicz norm, the Luxemburg norm, and the $p$-Amemiya norms separately.