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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.

The almost Dunford-Pettis property of semi-compact operators

Aqzzouz B., Elbour A.

Demonstratio Mathematica

2012

Vol. 45, nr 1

129-142

We establish necessary and sufficient conditions for which each positive semi-compact operator (resp. the second power of a positive semi-compact operator) is almost Dunford-Pettis (resp. Dunford-Pettis).

Semi-compactness of Almost Dunford-Pettis operators on Banach lattices

Aqzzouz B., Elbour A.

Demonstratio Mathematica

2011

Vol. 44, nr 1

131-141

We study the semi-compactness of positive Almost Dunford–Pettis (resp. the square of positive Almost Dunford–Pettis) operators on Banach lattices and we give some consequences.

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.