The duality problem for the class of b-weakly compact operators
type: Item
instance of: scholarly article
title: The duality problem for the class of b-weakly compact operators
zbMATH Open document ID: 1191.47024
author: Belmesnaoui Aqzzouz
author: Aziz Elbour
author: Jawad H'Michane
published in: Positivity
publication date: 2009-12-02T00:00:00Z
review text: Let \(E\) be a Banach lattice and let \(E^{\sim}\) be the order dual of \(E\). Assume that \(E^{\sim}\) separates \(E\). A subset \(U\) of \(E\) is b-order bounded provided that \(A\) is bounded in the second order dual \(E^{\sim\sim}\). If \(X\) is a Banach space and \(T:E\to X\) carries each b-order bounded subset of \(E\) into a weakly compact subset of \(X\), then \(T\) is called weakly b-order compact. The authors study the interrelation between the weak-b-order compactness of an operator and its dual.
Mathematics Subject Classification ID: 47B07
Mathematics Subject Classification ID: 46A40
Mathematics Subject Classification ID: 46B40
zbMATH DE Number: 5641602
zbMATH Keywords: b-weakly compact operator
zbMATH Keywords: order dual
reviewed by: S. S. Kutateladze
MaRDI profile type: Publication
full work available at URL: s11117-008-2288-6
OpenAlex ID: W2162207681
cites work: Q4186829
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cites work: Q5491574
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cites work: Q5690471
DOI: 10.1007/S11117-008-2288-6
description: scientific article; zbMATH DE number 5641602