Subprojective Nakano spaces
type: Item
instance of: scholarly article
title: Subprojective Nakano spaces
zbMATH Open document ID: 1383.46010
author: César Ruiz
author: Victor Sanchez
published in: Journal of Mathematical Analysis and Applications
publication date: 2017-11-02T00:00:00Z
review text: Recall that a Banach space \(X\) is said to be subprojective if every infinite-dimensional subspace of \(X\) has an infinite-dimensional subspace which is complemented in \(X\). The authors prove that separable Nakano sequence spaces \(\ell_{(p_{n})}\) are subprojective. Moreover, by using the results of \textit{F. L. Hernández} and \textit{C. Ruiz} [J. Math. Anal. Appl. 389, No. 2, 899--907 (2012; Zbl 1257.46012)] on subspaces of separable Nakano function spaces, they show that \(L^{p(\cdot)}\) is subprojective if and only if it does not contain a subspace isomorphic to \(l_{q}\) with \(q<2\).
Mathematics Subject Classification ID: 46B03
Mathematics Subject Classification ID: 46B45
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 6802316
zbMATH Keywords: Nakano space
zbMATH Keywords: subprojectivity
reviewed by: Elói M. Galego
MaRDI profile type: Publication
full work available at URL: j.jmaa.2017.09.014
OpenAlex ID: W2754616240
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DOI: 10.1016/J.JMAA.2017.09.014
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description: scientific article; zbMATH DE number 6802316