A gliding hump property and banach-mackey spaces
Author
Swartz, Charles
Full text
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/151010.4067/S0716-09172001000200007
Abstract
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.