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

 

Compactness properties of operators dominated by AM-compact operators


Authors: Belmesnaoui Aqzzouz, Redouane Nouira and Larbi Zraoula
Journal: Proc. Amer. Math. Soc. 135 (2007), 1151-1157
MSC (2000): Primary 46A40, 46B40, 46B42
Published electronically: October 13, 2006
Erratum: Proc. Amer. Math. Soc. 137 (2009), 2813-2815
MathSciNet review: 2262919
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Abstract: We study several properties about the problem of domination in the class of positive AM-compact operators, and we obtain some interesting consequences on positive compact operators. Also, we give a sufficient condition under which a Banach lattice is discrete.


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Additional Information

Belmesnaoui Aqzzouz
Affiliation: Département de Mathématiques, Faculté des Sciences, Université Ibn Tofail, Equipe d’Analyse Fonctionnelle, B.P. 133, Kénitra, Morocco
Email: baqzzouz@hotmail.com

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

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

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08585-6
PII: S 0002-9939(06)08585-6
Keywords: AM-compact operator, order continuous norm, discrete vector lattice.
Received by editor(s): July 7, 2005
Received by editor(s) in revised form: November 14, 2005
Published electronically: October 13, 2006
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2006 American Mathematical Society