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.

## Abstract

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 |
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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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