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Application of $(L)$ sets to some classes of operators

Kamal El Fahri; Nabil Machrafi; Jawad H'michane; Aziz Elbour — 2016

Mathematica Bohemica

The paper contains some applications of the notion of $Ł$ sets to several classes of operators on Banach lattices. In particular, we introduce and study the class of order $(L)$ -Dunford-Pettis operators, that is, operators from a Banach space into a Banach lattice whose adjoint maps order bounded subsets to an $(L)$ sets. As a sequence characterization of such operators, we see that an operator $T : X \to E$ from a Banach space into a Banach lattice is order $Ł$ -Dunford-Pettis, if and only if $| T (x_{n}) | \to 0$ for $σ (E, E^{'})$ for every weakly null...

On the class of order almost L-weakly compact operators

Kamal El Fahri; Hassan Khabaoui; Jawad Hmichane — 2022

Commentationes Mathematicae Universitatis Carolinae

We introduce a new class of operators that generalizes L-weakly compact operators, which we call order almost L-weakly compact. We give some characterizations of this class and we show that this class of operators satisfies the domination problem.

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Application of ( L ) sets to some classes of operators

On the class of order almost L-weakly compact operators

Application of $(L)$ sets to some classes of operators