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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 algebra ideals of regular operators

Bayram E. B., Wnuk W.

Commentationes Mathematicae

2013

Vol. 53, No. 2

127--133

We investigate relationships joining the order continuity of a norm in a Banach lattice and some composition properties of L-weakly and M-weakly compact operators. Our results improve Proposition 3.6.16 from [5].

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.