El Fahri, K. and H'michane, J. and El Kaddouri, A. and Aboutafail, O.
(2017)
*On the weak compactness of weak* Dunford-Pettis operators on Banach lattices.*
Advances in Operator Theory, 2 (3).
pp. 192-200.

## Abstract

We characterize Banach lattices on which each positive weak* Dunford-Pettis operator is weakly (resp., M-weakly, resp., order weakly) compact. More precisely, we prove that if F is a Banach lattice with order continuous norm, then each positive weak* Dunford-Pettis operator T: E → F is weakly compact if, and only if, the norm of E0 is order continuous or F is reflexive. On the other hand, when the Banach lattice F is Dedekind σ-complete, we show that every positive weak* Dunford-Pettis operator T: E → F is M-weakly compact if, and only if, the norms of E0 and F are order continuous or E is finite-dimensional. © 2016 by the Tusi Mathematical Research Group.

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/3943 |

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