Lineability in subsets of measure and function spaces
type: Item
instance of: scholarly article
title: Lineability in subsets of measure and function spaces
zbMATH Open document ID: 1147.46021
published in: Linear Algebra and its Applications
publication date: 2008-05-15T00:00:00Z
review text: A subset \(M\) of a function space is called lineable (or \(c\)-lineable) if \(M\cup \{0\}\) contains an infinite dimensional linear subspace (or, respectively, a linear subspace of dimension \(c\)). The main results are the following. Let \(1\leq p <q\). Then \(L^p[0,1]\setminus L^q[0,1]\) is \(c\)-lineable. If \(I\) is an unbounded interval, then \(L^q(I)\setminus L^p(I)\) is \(c\)-lineable. \(l_q\setminus l_p\) is \(c\)-lineable. Let \(\lambda\) be the Lebesgue measure on the Borel sets in \([0,1]\) and \(X\) an infinite dimensional Banach space. Then the set of injective measures is lineable in \(ca(\lambda,X)\). The set of measures whose range is neither closed nor convex is lineable in \(ca(\lambda,X)\). If \(\overline{\lambda}\) is the Lebesgue measure on the measurable subsets of \([0,1]\) and \(1\leq p<\infty\), then the set of \(l_p\)-valued measures with relatively compact range and such that their total variation is \(\infty\) on every non-null set is lineable in \(cca(\overline{\lambda},l_p)\).
reviewed by: Hans Weber
Mathematics Subject Classification ID: 46B99
Mathematics Subject Classification ID: 46E27
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 28A33
zbMATH DE Number: 5275766
zbMATH Keywords: lineability
zbMATH Keywords: measure spaces
zbMATH Keywords: function spaces
zbMATH Keywords: injective measures
author: G. A. Muñoz-Fernández
author: Niklas Palmberg
author: Daniele Puglisi
author: J. B. Seoane-Sepúlveda
MaRDI profile type: Publication
full work available at URL: j.laa.2008.01.008
OpenAlex ID: W2105059684
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DOI: 10.1016/J.LAA.2008.01.008
description: scientific article; zbMATH DE number 5275766