El Fahri, K. and Machrafi, N. and H’Michane, J. and Elbour, A. (2016) Application of (L) sets to some classes of operators. Mathematica Bohemica, 141 (3). pp. 327-338.

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The paper contains some applications of the notion of (L) 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 → E from a Banach space into a Banach lattice is order (L)-Dunford-Pettis, if and only if |T (xn)| → 0 for σ(E, Eʹ) for every weakly null sequence (xn) ⊂ X. We also investigate relationships between order (L)-Dunford-Pettis, AM-compact, weak* Dunford-Pettis, and Dunford-Pettis operators. In particular, it is established that each operator T: E → F between Banach lattices is Dunford-Pettis whenever it is both order (L)-Dunford-Pettis and weak* Dunford-Pettis, if and only if E has the Schur property or the norm of F is order continuous. © 2016, Akademie ved Ceske Republiky. All rights reserved.

Item Type: Article
Subjects: Mathematics
Divisions: SCIENTIFIC PRODUCTION > Mathematics
Depositing User: Administrateur Eprints Administrateur Eprints
Last Modified: 31 Jan 2020 15:48
URI: http://eprints.umi.ac.ma/id/eprint/3986

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