Orlicz spaces which are Riesz isomorphic to \(\ell ^{\infty}\)
Let \(L^{\phi}(S,\Sigma,\mu)\) be an Orlicz space. When \(\mu\) is a \(\sigma\)-finite purely atomic measure, or \(S={\mathbb{Z}}^+\), \(\Sigma\) is the \(\sigma\)-algebra of all subsets of \({\mathbb{Z}}^+\), \(\mu (\{n\})=a_ n\), we write \(\ell^{\phi}(a_ n)\). The author gives necessary and sufficient conditions, in terms of \(\phi\) and \(a_ n\), for \(\ell^{\phi}(a_ n)\) to be Riesz isomorphic to \(\ell^{\infty}\). Consider certain classes of sequences \((a_ n)\) such that \(\ell^{\phi}(a_ n)\) is Riesz isomorphic to \(\ell^{\infty}\). The thickness in the sense of Baire category of such classes is also discussed.
thickness in the sense of Baire category
scientific article; zbMATH DE number 4088273