On the weak compactness of b-weakly compact operators
type: Item
instance of: scholarly article
title: On the weak compactness of b-weakly compact operators
zbMATH Open document ID: 1198.47034
author: Belmesnaoui Aqzzouz
author: Aziz Elbour
published in: Positivity
publication date: 2010-04-13T00:00:00Z
review text: In this paper, the aim of the authors is to prove that each b-weakly compact operator \(T\) from a Banach lattice \(E\) into a Banach space \(X\) is weakly compact if and only if the norm of dual space \(E'\) is order continuous or \(X\) is reflexive. As a result, they give some characterizations of the order continuity of the dual norm and a characterization of reflexive Banach lattices. They also give a necessary and sufficient condition under which the second power of a b-weakly compact operator is weakly compact.
reviewed by: Ömer Gök
Mathematics Subject Classification ID: 47B07
Mathematics Subject Classification ID: 46B42
Mathematics Subject Classification ID: 47B60
zbMATH DE Number: 5692401
zbMATH Keywords: b-order bounded set
zbMATH Keywords: b-weakly compact operator
zbMATH Keywords: Banach lattice
zbMATH Keywords: weakly compact operator
zbMATH Keywords: AM-spaces
zbMATH Keywords: AL-space
zbMATH Keywords: order continuous norm
zbMATH Keywords: Schur property
MaRDI profile type: Publication
full work available at URL: s11117-009-0006-7
OpenAlex ID: W2078799337
cites work: Q5491574
cites work: On property (b) of vector lattices
cites work: A note on Riesz spaces with property-b
cites work: A note on \(b\)-weakly compact operators
cites work: Characterizations of Riesz spaces with \(b\)-property
cites work: On \(b\)-weakly compact operators on Banach lattices
cites work: The duality problem for the class of b-weakly compact operators
cites work: Banach lattices
cites work: Q4049667
cites work: Q3669960
DOI: 10.1007/S11117-009-0006-7
description: scientific article; zbMATH DE number 5692401