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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Semi-compactness of positive Dunford-Pettis operators on Banach lattices


Authors: Belmesnaoui Aqzzouz, Redouane Nouira and Larbi Zraoula
Journal: Proc. Amer. Math. Soc. 136 (2008), 1997-2006
MSC (2000): Primary 46A40, 46B40, 46B42
Published electronically: February 19, 2008
MathSciNet review: 2383506
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Abstract: We investigate Banach lattices on which each positive Dunford-Pettis operator is semi-compact and the converse. As an interesting consequence, we obtain Theorem 2.7 of Aliprantis-Burkinshaw and an element of Theorem 1 of Wickstead.


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Additional Information

Belmesnaoui Aqzzouz
Affiliation: Département d’Economie, Faculté des Sciences Economiques, Juridiques et Sociales, Université Mohammed V-Souissi, B.P. 5295, Sala Eljadida, Morocco
Email: baqzzouz@hotmail.com

Redouane Nouira
Affiliation: Université Ibn Tofail, Faculté des Sciences, Département de Mathématiques, B.P. 133, Kénitra, Morocco

Larbi Zraoula
Affiliation: Université Ibn Tofail, Faculté des Sciences, Département de Mathématiques, B.P. 133, Kénitra, Morocco

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09032-1
PII: S 0002-9939(08)09032-1
Keywords: Semi-compact operator, Dunford--Pettis operator, order continuous norm, discrete vector lattice
Received by editor(s): February 24, 2006
Received by editor(s) in revised form: December 2, 2006
Published electronically: February 19, 2008
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2008 American Mathematical Society