MATHEMATICA BOHEMICA, Vol. 136, No. 1, pp. 105-112, 2011

Some characterizations of order
weakly compact operator

Belmesnaoui Aqzzouz, Aziz Elbour

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

Abstract: We introduce the notion of order weakly sequentially continuous lattice operations of a Banach lattice, use it to generalize a result regarding the characterization of order weakly compact operators, and establish its converse. Also, we derive some interesting consequences.

Keywords: order weakly compact operator, order continuous norm, discrete Banach lattice, weakly sequentially continuous lattice operations

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

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