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Weak precompactness, strong boundedness, and weak complete continuity

Published online by Cambridge University Press:  24 October 2008

Catherine A. Abbott ,
Elizabeth M. Bator ,
Russell G. Bilyeu  and
Paul W. Lewis
Catherine A. Abbott
Affiliation:
University of North Texas, Denton, Texas, U.S.A.
Elizabeth M. Bator
Affiliation:
University of North Texas, Denton, Texas, U.S.A.
Russell G. Bilyeu
Affiliation:
University of North Texas, Denton, Texas, U.S.A.
Paul W. Lewis
Affiliation:
University of North Texas, Denton, Texas, U.S.A.
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Abstract

Weak precompactness in spaces of vector measures and in the space of Bochner integrable functions is studied. Uniform countable additivity and uniform integrability are characterized in terms of weak precompactness. Through this, a connection between strongly bounded operators and operators having weakly precompact adjoints on abstract continuous function spaces is established. These operators are compared with weakly completely continuous operators.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 108 , Issue 2 , September 1990 , pp. 325 - 335
Copyright
Copyright © Cambridge Philosophical Society 1990

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