Weak sequential completeness of Orlicz spaces (Q1379852)

Let \(L^\varphi\) be an Orlicz space defined by a finite valued Orlicz function (not necessarily convex) over a complete \(\sigma\)-finite atomless measure space \((\Omega,\Sigma,\mu)\) (resp. \(\Omega= N\) with \(\mu\) being the counting measure). It is proved that \(L^\varphi\) is sequentially weakly complete if and only if \(\varphi\) is equivalent to some convex Orlicz function and \(\varphi\in\Delta_2\) (resp. \(\varphi\in\Delta^0_2\)).