A. Elbour

orcid.org/0000-0002-8431-911X
Search this author in Google Scholar

Articles: 3

Limited and Dunford-Pettis operators on Banach lattices

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

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

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.