Some properties of the class of positive Dunford--Pettis operators
type: Item
instance of: scholarly article
title: Some properties of the class of positive Dunford--Pettis operators
zbMATH Open document ID: 1167.47033
author: Belmesnaoui Aqzzouz
author: Aziz Elbour
author: Jawad H'Michane
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-05-13T00:00:00Z
review text: The authors establish necessary and sufficient conditions for positive Dunford--Pettis operators to be M-weakly compact (respectively, L-weakly compact). They first prove that each Dunford--Pettis operator \(T\) from a Banach lattice \(E\) into a Banach space \(F\) is M-weakly compact if and only if the norm dual \(E'\) of \(E\) is order continuous or \(F=\{0\}\). Next, they establish an analogue of the Riesz theorem by proving that the closed unit ball \(B_{E}\) of a Banach lattice \(E\) is L-weakly compact if and only if \(E\) is finite-dimensional. From this, they deduce some interesting results.
reviewed by: Ömer Gök
Mathematics Subject Classification ID: 47B65
Mathematics Subject Classification ID: 46B42
zbMATH DE Number: 5553675
zbMATH Keywords: Dunford-Pettis Operators
zbMATH Keywords: compact operators
zbMATH Keywords: M-weakly compact operators
zbMATH Keywords: L-weakly compact operators
zbMATH Keywords: Banach lattice
zbMATH Keywords: weakly compact operators
zbMATH Keywords: order continuous norm
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.12.063
OpenAlex ID: W1971295131
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cites work: Banach lattices
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DOI: 10.1016/J.JMAA.2008.12.063
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description: scientific article; zbMATH DE number 5553675