Ideal-triangularizability of semigroups of positive operators
type: Item
instance of: scholarly article
title: Ideal-triangularizability of semigroups of positive operators
zbMATH Open document ID: 1233.47034
author: Roman Drnovšek
author: Marko Kandić
published in: Integral Equations and Operator Theory
publication date: 2009-11-13T00:00:00Z
review text: A positive operator \(T\) acting on a Banach lattice \(E\) is called ideal-triangularizable if it admits a maximal chain of invariant closed ideals of \(E\). The paper under review discusses the question under which conditions a multiplicative semigroup \(\mathcal{S}\) of ideal-triangularizable operators is simultaneously ideal-triangularizable. For example, it is proved that this is the case when \(E\) has order continuous norm. Also, a semigroup \(\mathcal{S}\) of positive compact operators on a Banach lattice with order continuous norm is ideal-triangularizable if and only if every pair \(\{S,T\}\) of operators in \(\mathcal{S}\) is ideal-triangularizable.
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 47A46
Mathematics Subject Classification ID: 47A15
Mathematics Subject Classification ID: 47B65
zbMATH DE Number: 5633116
zbMATH Keywords: invariant subspaces
zbMATH Keywords: Banach lattices
zbMATH Keywords: closed ideals
zbMATH Keywords: positive operators
zbMATH Keywords: abstract integral operators
zbMATH Keywords: semigroups of operators
MaRDI profile type: Publication
full work available at URL: s00020-009-1705-y
OpenAlex ID: W2090888896
DOI: 10.1007/S00020-009-1705-Y
description: scientific article; zbMATH DE number 5633116