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We characterize Banach lattices on which every positive almost Dunford-Pettis operator is weakly compact.
We establish necessary and sufficient conditions under which weak Banach-Saks operators are weakly compact (respectively, L-weakly compact; respectively, M-weakly compact). As consequences, we give some interesting characterizations of order continuous norm (respectively, reflexive Banach lattice).
We characterize Banach lattices on which every weak Banach-Saks operator is b-weakly compact.
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