Abstract
In this paper, we show that for a pair of Banach lattices E and F with E Dedekind σ-complete, the following statements are equivalent:(1)Each positive U-Dunford-Pettis (respectively, Dunford-Pettis) operator T:E→F is AM-compact;(2)Either the norm of E is order continuous or else F is discrete and the norm of F is order continuous.If, in addition, F has the weak Dunford-Pettis property, then each U-Dunford-Pettis (respectively, Dunford-Pettis) operator T:E→F is AM-compact if and only if either the norm of E is order continuous or else F has the Schur property. As a consequence, we obtain some new characterizations of Banach lattices with order continuous norms (respectively, with the Schur property).
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