Weak compactness of almost L-weakly and almost M-weakly compact operators. Issue 9 (2nd September 2021)

• Record Type: Journal Article
• Authors: Afkir, Farid; Bouras, Khalid; Elbour, Aziz; El Filali, Safae
• Is Part Of: Quaestiones mathematicae. Volume 44:Issue 9(2021)
• Page Start: 1145
• Page End: 1154
• Publication Date: 2021-09-02
• Subjects: Primary: 46B07 -- Secondary: 46B42 -- 47B50; Almost L-weakly compact operator -- almost M-weakly compact operator -- M- weakly compact operator -- L-weakly compact operator -- Banach lattice -- order continuous norm; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2020.1777482
• Languages: English
• ISSNs: 1607-3606

Abstract

Abstract: In this paper, we investigate conditions on a pair of Banach lattices E and F that tells us when every positive almost L-weakly compact (resp. almost M- weakly compact) operator T : E → F is weakly compact. Also, we present some necessary conditions that tells us when every weakly compact operator T : E → F is almost M-weakly compact (resp. almost L-weakly compact). In particular, we will prove that if every weakly compact operator from a Banach lattice E into a Banach space X is almost L-weakly compact, then E is a KB-space or X has the Dunford-Pettis property and the norm of E is order continuous.