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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.20 n.2 Antofagasta ago. 2001

http://dx.doi.org/10.4067/S0716-09172001000200007 

A GLIDING HUMP PROPERTY AND
BANACH-MACKEY SPACES

CHARLES SWARTZ

New Mexico State University - U. S. A.

 

Abstract

We consider the Banach-Mackey property for pairs of vector spaces E and E' 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 anoter 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.

 

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Received : December, 2000.

Charles Swartz

Department of Mathematical Sciences

New Mexico State University

Las Cruces, NM 88003

USA

E-mail: cswartz@nmsu.edu