A Banach-lattice version of the Josefson-Nissenzweig theorem

• Autores: Marek Wójtowicz
• Localización: Indagationes mathematicae, ISSN 0019-3577, Vol. 18, Nº 3, 2007, págs. 479-484
• Idioma: inglés
• DOI: 10.1016/s0019-3577(07)80036-x
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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).