Geodesic
M-weak and L-weak compactness of b-weakly compact operators
Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 3, pp. 367-375.

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We characterize Banach lattices under which each b-weakly compact (resp. b-AM-compact, strong type (B)) operator is L-weakly compact (resp. M-weakly compact).
Classification : 46A40, 46B40, 46B42
Keywords: b-weakly compact operator; b-AM-compact operator; strong type (B) operator; order continuous norm; positive Schur property 
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H'Michane, J.; El Kaddouri, A.; Bouras, K.; Moussa, M. M-weak and L-weak compactness of b-weakly compact operators. Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 3, pp. 367-375. http://geodesic.mathdoc.fr/item/CMUC_2013__54_3_a4/