Invariant subspaces of operators on \(\ell_ p\)-spaces
type: Item
instance of: scholarly article
title: Invariant subspaces of operators on \(\ell_ p\)-spaces
zbMATH Open document ID: 0819.47006
published in: Journal of Functional Analysis
publication date: 1994-03-14T00:00:00Z
review text: The authors prove interesting, and potentially useful, invariant subspace results for positive operators on \(\ell^ p\) that are quasinilpotent at a non-zero positive point \(x_ 0\) (i.e., \(\lim_{n\to\infty} \| T^ n x_ 0\|^{1/n}= 0\) and all entries \(t_{ij}\) of the matrix for \(T\) and all coordinates of \(x_ 0\) are non-negative). Such an operator must have a non-trivial complemented closed invariant subspace. More generally, they prove that for such a \(T\) and for any bounded double sequence of complex numbers \(\{w_{ij}\}\), the operator defined by the weighted infinite matrix \([w_{ij} t_{ij}]\) has a non-trivial invariant subspace.
Mathematics Subject Classification ID: 47A15
Mathematics Subject Classification ID: 47B37
zbMATH DE Number: 515236
zbMATH Keywords: invariant subspace results
zbMATH Keywords: positive operators on \(\ell^ p\)
zbMATH Keywords: quasinilpotent at a non-zero positive point
zbMATH Keywords: non-trivial complemented closed invariant subspace
author: Y. A. Abramovich
author: Charalambos D. Aliprantis
author: Owen Burkinshaw
reviewed by: Jeffrey R. Butz
MaRDI profile type: Publication
full work available at URL: jfan.1993.1097
OpenAlex ID: W2001288205
DOI: 10.1006/JFAN.1993.1097
description: scientific article; zbMATH DE number 515236