A gliding hump property and banach-mackey spaces

• Swartz, Charles ^[1]
  1. [1] New Mexico State University

     New Mexico State University

     Estados Unidos

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 20, Nº. 2, 2001, págs. 243-261
• Idioma: inglés
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• Resumen

  • We consider the Banach–Mackey property for pairs of vector spaces E and E0 which are in duality. Let A be an algebra of sets and assume that P is an additive map from A into the projection operators on E. We define a continuous gliding hump property for the map P and show that pairs with this gliding hump property and another measure theoretic property are Banach-Mackey pairs, i. e., weakly bounded subsets of E are strongly bounded. Examples of vector valued function spaces, such as the space of Pettis integrable functions, which satisfy these conditions are given.