On \(\ell ^ p\)-complemented copies in Orlicz spaces
type: Item
instance of: scholarly article
title: On \(\ell ^ p\)-complemented copies in Orlicz spaces
zbMATH Open document ID: 0659.46020
DOI: 10.1007/BF02767352
author: Francisco L. Hernández
author: Baltasar Rodríguez-Salinas
published in: Israel Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Let \(1\leq \alpha \leq \beta <\infty\) and let F be a closed subset of [\(\alpha\),\(\beta\) ]. If \(\alpha >1\) (resp. \(\alpha =1)\), then there is an Orlicz sequence space \(\ell^{\phi}\) with indices \(\alpha_{\phi}=\alpha\) and \(\beta_{\phi}=\beta\) which contains a complemented copy of \(\ell^ p\) if and only if \(p\in F\) (resp. \(p\in F\cup \{1\})\). Similar results remain true also for Orlicz function spaces. A recent result of the first author and \textit{V. Peirats} [Isr. J. Math. 56, 355-360 (1986; Zbl 0631.46030)] concerning the existence of a minimal Orlicz space \(L^{\phi}(\mu)\) with no complemented copy of \(\ell^ p\) for any \(p\neq 2\) is proved.
Mathematics Subject Classification ID: 46B25
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 4078002
zbMATH Keywords: Orlicz sequence
zbMATH Keywords: Orlicz function spaces
zbMATH Keywords: existence of a minimal Orlicz space
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02767352
OpenAlex ID: W2057514491
description: scientific article; zbMATH DE number 4078002