Orlicz spaces which are Riesz isomorphic to \(\ell ^{\infty}\)
type: Item
instance of: scholarly article
title: Orlicz spaces which are Riesz isomorphic to \(\ell ^{\infty}\)
zbMATH Open document ID: 0665.46020
DOI: 10.1216/RMJ-1988-18-1-185
author: Witold Wnuk
published in: Rocky Mountain Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: 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.
reviewed by: Peng-Yee Lee
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 46B25
zbMATH DE Number: 4088273
zbMATH Keywords: Orlicz space
zbMATH Keywords: thickness in the sense of Baire category
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4088273