Approximate compactness in Orlicz spaces (Q1268714)

Let \(M\) be a convex \(N\)-function and let \(\ell^M\) be the Orlicz sequence space with Luxemburg norm, \(L^M\) the Orlicz space with Luxemburg norm or with Orlicz norm of functions over a Lebesgue measurable set \(\Omega\subset \mathbb{R}\) of finite measure. It is proved that \(\ell^M\) is approximatively compact if and only if it is reflexive and \(L^M\) is approximatively compact if and only if it is reflexive and rotund.