Abstract
Let E, F be two Banach lattices with E order continuous. If F can be mapped positively onto E then the dual F * contains a weak * -null sequence of positive and norm-one elements (Theorem 1). This is a Banach-lattice version of the classical Josefson-Nissenzweig theorem. It is an immediate consequence of the dual characterization of order continuity: E is order continuous iff E is Dedekind complete and every norm-one and pairwise disjoint sequence in E * is weak *-null (Theorem 2).
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