MATHEMATICA BOHEMICA, Vol. 137, No. 3, pp. 347-354, 2012

On the equality between some classes of operators on Banach lattices

Belmesnaoui Aqzzouz, Aziz Elbour, Mohammed Moussa

Belmesnaoui Aqzzouz, Université Mohammed V-Souissi, Faculté des Sciences Economiques, Juridiques et Sociales, Département d'Economie, B.P. 5295, SalaAljadida, Morocco, e-mail: baqzzouz@hotmail.com; Aziz Elbour, Mohammed Moussa, Université Ibn Tofail, Faculté des Sciences, Departement de Mathématiques, B.P. 133, Kénitra, Morocco

Abstract: We establish some sufficient conditions under which the subspaces of Dunford-Pettis operators, of M-weakly compact operators, of L-weakly compact operators, of weakly compact operators, of semi-compact operators and of compact operators coincide and we give some consequences.

Keywords: M-weakly compact operator, L-weakly compact operator, Dunford-Pettis operator, weakly compact operator, semi-compact operator, compact operator, order continuous norm, discrete Banach lattice, positive Schur property

Classification (MSC 2010): 46A40, 46B40, 46B42

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