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International Journal of Mathematics and Mathematical Sciences
Volume 2011, Article ID 609287, 12 pages
http://dx.doi.org/10.1155/2011/609287
Research Article

Duality Property for Positive Weak Dunford-Pettis Operators

1Département d'Economie, Faculté des Sciences Economiques, Juridiques et Sociales, Université Mohammed V-Souissi, BP 5295, Sala Al Jadida, Morocco
2Département de Mathématiques, Faculté des Sciences, Université Ibn Tofail, BP 133, Kénitra, Morocco

Received 15 December 2010; Accepted 5 May 2011

Academic Editor: Yuri Latushkin

Copyright © 2011 Belmesnaoui Aqzzouz et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove that an operator is weak Dunford-Pettis if its adjoint is one but the converse is false in general, and we give some necessary and sufficient conditions under which each positive weak Dunford-Pettis operator has an adjoint which is weak Dunford-Pettis.