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We introduce and study the class of unbounded Dunford--Pettis operators. As consequences, we give basic properties and derive interesting results about the duality, domination problem and relationship with other known classes of operators.
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).
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