On \(\ell^ p\)-copies in Musielak-Orlicz sequence spaces
type: Item
instance of: scholarly article
title: On \(\ell^ p\)-copies in Musielak-Orlicz sequence spaces
zbMATH Open document ID: 0728.46015
DOI: 10.1007/BF01191882
author: Vicente Peirats
author: César Ruiz
published in: Archiv der Mathematik
publication date: 1992-01-01T00:00:00Z
review text: We study \(\ell^ p\)-copies in Musielak-Orlicz sequence spaces \(\ell^ M\) also called modular sequence spaces. We present a necessary condition on the function \(x^ p\) in order that \(\ell^ p\) can be isomorphic to a subspace of a Musielak-Orlicz sequence space \(\ell^ M\). As application, we characterize the \(\ell^ p\)-copies in Nakano sequence spaces \(\ell^{(p_ n)}\). Namely, if \(0<\inf_{n}\{p_ n)\leq \sup_{n}\{p_ n\}<\infty\), then \(\ell^ p\) is isomorphic to a (complemented) subspace of \(\ell^ p\) if and only if p is an accumulation point of \((p_ n)^{\infty}_{n=1}\).
Mathematics Subject Classification ID: 46A80
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 4203053
zbMATH Keywords: \(\ell ^ p\)-copies in Musielak-Orlicz sequence spaces \(\ell ^ M\)
zbMATH Keywords: modular sequence spaces
zbMATH Keywords: Nakano sequence spaces
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4203053