Weak limited sets and operators on Banach lattices. Issue 1 (2nd January 2023) - Afkir, Farid; Elbour, Aziz
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.