Dunford-Pettis property of the product of some operators
type: Item
instance of: scholarly article
zbMATH Open document ID: 1249.47020
author: Belmesnaoui Aqzzouz
author: Aboutafail Othman
author: Aziz Elbour
publication date: 2012-07-16T00:00:00Z
Mathematics Subject Classification ID: 47B65
Mathematics Subject Classification ID: 46B42
zbMATH DE Number: 6056398
zbMATH Keywords: Banach lattice
zbMATH Keywords: Dunford-Pettis operator
zbMATH Keywords: order bounded operator
zbMATH Keywords: order weakly compact operator
MaRDI profile type: Publication
title: Dunford-Pettis property of the product of some operators
published in: Methods of Functional Analysis and Topology
review text: An operator \(T\) from a Banach lattice \(E\) into a Banach space \(X\) is called almost Dunford-Pettis if \(\| T(x_n)\| \to 0\) for every disjoint sequence \(\{ x_n\}\subset E\) such that \(x_n\to 0\) in the \(\sigma (E,E')\) topology. An operator between two Banach spaces is called Dunford-Pettis if it maps weakly null sequences into norm null sequences. The authors establish a sufficient condition for the product of an order bounded almost Dunford-Pettis operator and an order weakly compact operator to be Dunford-Pettis. Several applications are given, in particular a generalization of a result by \textit{W. Wnuk} [Atti Semin. Mat. Fis. Univ. Modena 42, No. 1, 227--236 (1994; Zbl 0805.46023)].
reviewed by: Anatoly N. Kochubei
description: scientific article; zbMATH DE number 6056398