Asymptotic behavior of positive operators on Banach lattices
type: Item
instance of: scholarly article
title: Asymptotic behavior of positive operators on Banach lattices
zbMATH Open document ID: 0984.47029
DOI: 10.1023/A:1009870310048
published in: Positivity
publication date: 2002-05-14T00:00:00Z
review text: This is a nice short survey dealing with some asymptotic properties of positive operators on Banach lattices. The new results are provided with sketches of proofs. A sample result: Theorem 12. Let \(0\leq S\leq T\) be two operators on a Banach lattice \(E\) with order continuous norm. If \(T\) is strongly stable (resp. almost periodic), then \(S\) has the same property. Recall that an operator \(T\) is strongly stable (resp. almost periodic) if for each \(x\in E\) the sequence \(\{T^nx\}\) converges in norm (resp. is norm-precompact). The paper contains a number of open problems.
Mathematics Subject Classification ID: 47B65
Mathematics Subject Classification ID: 46B42
zbMATH DE Number: 1538732
zbMATH Keywords: asymptotic properties
zbMATH Keywords: positive operators on Banach lattices
zbMATH Keywords: order continuous norm
zbMATH Keywords: strongly stable
zbMATH Keywords: almost periodic
zbMATH Keywords: norm-precompact
author: Eduard Yu. Emel'yanov
author: Frank Räbiger
author: Manfred P. H. Wolff
reviewed by: Y. A. Abramovich
MaRDI profile type: Publication
full work available at URL: a:1009870310048
OpenAlex ID: W202405280
description: scientific article; zbMATH DE number 1538732