Orlicz function spaces without complemented copies of \(\ell ^ p\)
type: Item
instance of: scholarly article
title: Orlicz function spaces without complemented copies of \(\ell ^ p\)
zbMATH Open document ID: 0631.46030
DOI: 10.1007/BF02782943
author: Francisco L. Hernández
author: Vicente Peirats
published in: Israel Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: The existence of reflexive Orlicz sequence spaces \(\ell^{\phi}\) containing no complemented subspaces isomorphic to \(\ell^ n\)-space for any \(1\leq p<\infty\) was proved by \textit{J. Lindenstrauss} and \textit{L. Tzafriri} [Isr. J. Math. 11, 355-379 (1972; Zbl 0237.46034) and 14, 368- 389 (1973; Zbl 0262.46031), see also ``Classical Banach spaces I. Sequence spaces.'' (1977; Zbl 0362.46013)]. In this paper we give the corresponding result for Orlicz function spaces \(L^{\phi}[0,1]\). After introducing and studying the class of minimal Orlicz function spaces \(L^{\phi}[0,1]\) we prove the existence of reflexive Orlicz function spaces \(L^{\phi}[0,1]\) that contain no complemented subspaces isomorphic to \(\ell^ p\)-space for any \(1\leq p\neq 2<\infty\).
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 46B25
zbMATH DE Number: 4026115
zbMATH Keywords: complemented subspaces
zbMATH Keywords: Orlicz function spaces
zbMATH Keywords: minimal Orlicz function spaces
zbMATH Keywords: reflexive Orlicz function spaces
MaRDI profile type: Publication
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cites work: Q4136031
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description: scientific article; zbMATH DE number 4026115