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Weak and almost Dunford-Pettis operators on Banach lattices

Aqzzouz B., Bouras K.

Demonstratio Mathematica

2013

Vol. 46, nr 1

165--179

We introduce the class of Banach lattices with the AM-compactness property and we use it to characterize Banach lattices on which each positive weak Dunford–Pettis operator is almost Dunford–Pettis and conversely.

Some properties of positive weak Dunford-Pettis operators on Banach lattices

Aqzzouz B., Bourass K.

Demonstratio Mathematica

2009

Vol. 42, nr 4

817-823

We characterize Banach lattices for which each positive weak Dunford-Pettis operator is weakly compact. As consequences, we obtain some interesting results on reflexive Banach lattices.