Application of (L) sets to some classes of operators

Title:

Application of (L) sets to some classes of operators

Creator:

El Fahri, Kamal, Machrafi, Nabil, H'michane, Jawad, and Elbour, Aziz

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a9de285e-dc12-43ae-8e31-8a69628ab267
uuid:a9de285e-dc12-43ae-8e31-8a69628ab267
doi:10.21136/MB.2016.0076-14

Subject:

(L) set, order (L)-Dunford-Pettis operator, weakly sequentially continuous lattice operations, and Banach lattice

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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, E′ ) for every weakly null sequence (xn) ⊂ X. We also investigate relationships between order (L)-DunfordPettis, 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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

327-338

Source:

Mathematica bohemica | 2016 Volume:141 | Number:3

Harvested from:

CDK

Metadata only:

false