On the spectral radius of positive operators
type: Item
instance of: scholarly article
title: On the spectral radius of positive operators
zbMATH Open document ID: 0762.47012
DOI: 10.1007/BF02571448
author: Charalambos D. Aliprantis
author: Owen Burkinshaw
author: Y. A. Abramovich
published in: Mathematische Zeitschrift
publication date: 1993-03-07T00:00:00Z
full work available at URL: https://eudml.org/doc/174461
review text: We present several conditions which guarantee that a positive operator on a Banach lattice has a strictly positive spectral radius. The conditions are given in terms of commutativity properties. Sample results: \(\bullet\) Every positive operator that commutes with an ideal irreducible compact positive operator has a positive spectral radius. \(\bullet\) Every positive kernel operator that commutes with an order continuous band irreducible positive operator has a positive spectral radius. Some of these results can be proven by formulating a lattice hyperinvariant subspace theorem à la Lomonosov. The obtained results are either new or far reaching extensions of well known theorems. In the process of establishing our results, we also introduce several new classes of positive operators which satisfy a variety of irreducibility properties. These classes of operators are of independent interest on their own and they are classified and illustrated with many examples.
Mathematics Subject Classification ID: 47B65
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47A15
zbMATH DE Number: 126415
zbMATH Keywords: positive operator on a Banach lattice
zbMATH Keywords: strictly positive spectral radius
zbMATH Keywords: commutativity properties
zbMATH Keywords: positive kernel operator
zbMATH Keywords: order continuous band irreducible positive operator
zbMATH Keywords: lattice hyperinvariant subspace theorem
reviewed by: Y. A. Abramovich
MaRDI profile type: Publication
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OpenAlex ID: W2048210646
description: scientific article; zbMATH DE number 126415