Banach lattices of L-weakly and M-weakly compact operators

We give conditions for the linear span of the positive L-weakly compact (resp. M-weakly compact) operators to be a Banach lattice under the regular norm, for that Banach lattice to have an order continuous norm, to be an AL-space or an AM-space.Scientific and Technological Research Council of Turkey (TUBITAK)Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [2219]; Research Foundation of Namik Kemal UniversityNamik Kemal University [NKUBAP.00.10.AR.15.04]The first author was supported by The Scientific and Technological Research Council of Turkey (TUBITAK) within the context of 2219-Post Doctoral Fellowship Program and by the Research Foundation of Namik Kemal University (Project No. NKUBAP.00.10.AR.15.04.)