# A. Elbour

orcid.org/0000-0002-8431-911X

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### Limited and Dunford-Pettis operators on Banach lattices

Khalid Bouras, Abdennabi EL Aloui, Aziz Elbour

Methods Funct. Anal. Topology **25** (2019), no. 3, 205-210

This paper is devoted to investigation of conditions on a pair of Banach lattices $E; F$ under which every positive Dunford-Pettis operator $T:E\rightarrow F$ is limited. Mainly, it is proved that if every positive Dunford-Pettis operator $T:E\rightarrow F$ is limited, then the norm on $E'$ is order continuous or $F$ is finite dimensional. Also, it is proved that every positive Dunford-Pettis operator $T:E\rightarrow F$ is limited, if one of the following statements is valid:

1) The norm on $E^{\prime }$ is order continuous, and $F^{\prime }$ has weak$^{\ast }$ sequentially continuous lattice operations.

2) The topological dual $E^{\prime }$is discrete and its norm is
order continuous.

3) The norm of $E^{\prime }$ is order continuous and the lattice
operations in $E^{^{\prime }}$ are weak$^{\ast }$ sequentially continuous.

4) The norms of $E$ and of $E^{\prime }$ are order continuous.

### Some results on order bounded almost weak Dunford-Pettis operators

Nabil Machrafi, Aziz Elbour, Mohammed Moussa

Methods Funct. Anal. Topology **22** (2016), no. 3, 256-265

We give some new characterizations of almost weak Dunford-Pettis operators and we investigate their relationship with weak Dunford-Pettis operators.

### Dunford-Pettis property of the product of some operators

Belmesnaoui Aqzzouz, Othman Aboutafail, Aziz Elbour

Methods Funct. Anal. Topology **17** (2011), no. 4, 295-299

We establish a sufficient condition under which the product of an order bounded almost Dunford-Pettis operator and an order weakly compact operator is Dunford-Pettis. And we derive some consequences.