Geodesic
On $b$-order Dunford-Pettis operators and the $b$-$AM$-compactness property
Kazem Haghnejad Azar1 ; Razi Alavizadeh1 ; Kazem Haghnejad Azar ; Razi Alavizadeh
1Department of Mathematics and Applications, Faculty of Basic Sciences, University of Mohaghegh Ardabili, Ardabil, Iran
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 1, pp. 67-76 
Kazem Haghnejad Azar; Razi Alavizadeh; Kazem Haghnejad Azar; Razi Alavizadeh. On $b$-order Dunford-Pettis operators and the $b$-$AM$-compactness property. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 1, pp. 67-76. http://geodesic.mathdoc.fr/item/AMUC_2019_88_1_a5/
@article{AMUC_2019_88_1_a5,
     author = {Kazem Haghnejad Azar and Razi Alavizadeh and Kazem Haghnejad Azar and Razi Alavizadeh},
     title = { On $b$-order {Dunford-Pettis} operators and the $b$-$AM$-compactness property},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {67--76},
     year = {2019},
     volume = {88},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_1_a5/}
}
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Voir la notice de l'article provenant de la source Comenius University

‎In this paper‎, ‎we introduce $b$-order Dunford-Pettis operators‎, ‎that is‎, ‎an operator $T$ from a normed Riesz space $E$ into a Banach space $X$ is called $b$-order Dunford-Pettis if $T$ carries each $b$-order bounded subset of $E$ into a Dunford-Pettis subset of $X$‎, ‎and we investigate its relationship with order Dunford-Pettis operators‎. ‎We also introduce the $b$-$AM$-compactness property for a Banach lattice and we study some of its topological properties and its relationships with the Dunford-Pettis property‎. ‎We show that the identity operator of Banach lattice $E$ is $b$-order Dunford-Pettis if and only if $E$ has the $b$-$AM$-compactness property‎. ‎ We characterize Banach lattices $E$ and $F$ on which the adjoint of each operator from $E$ into $F$ which is $b$-order Dunford-Pettis and weak Dunford-Pettis‎, ‎is Dunford-Pettis‎.