Weak limited sets and operators on Banach lattices. Issue 1 (2nd January 2023)

• Record Type: Journal Article
• Authors: Afkir, Farid; Elbour, Aziz
• Is Part Of: Quaestiones mathematicae. Volume 46:Issue 1(2023)
• Page Start: 49
• Page End: 55
• Publication Date: 2023-01-02
• Subjects: Primary: 47B60 -- Secondary: 47B65 -- 46B42; Weak limited set -- weakly precompact set -- weak limited operator -- Dunford-Pettis operator -- Banach lattice -- order continuous norm; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2021.1990156
• Languages: English
• ISSNs: 1607-3606

Abstract

Abstract: In this paper, we prove that an operator T : E → F, between two Banach lattices, maps order intervals onto weak limited sets if and only if the modulus | ST | exists and is Dunford-Pettis for every Dunford-Pettis operator S : F → c 0. Next, we establish that a Banach lattice E does not contain any isomorphic copy of ℓ 1 if and only if the order intervals of E are weak limited and the norm of E ′ is order continuous. We also investigate the domination problem of the class of weak limited operators.