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Dual functors and the Radon-Nikodym property in the category of Banach spaces

Part of: Methods of category theory in functional analysis

Published online by Cambridge University Press:  09 April 2009

John Wick Pelletier
John Wick Pelletier
Affiliation:
Department of Mathematics York University, Keele Street Downsview, Ontario, Canada
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Abstract

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The notion of duality of functors is used to study and characterize spaces satisfying the Radon-Nikodym property. A theorem of equivalences concerning the Radon-Nikodym property is proved by categorical means; the classical Dunford-Pettis theorem is then deduced using an adjointness argument. The functorial properties of integral operators, compact operators, and weakly compact operators are discussed. It is shown that as an instance of Kan extension the weakly compact operators can be expressed as a certain direct limit of ordinary hom functors. Characterizations of spaces satisfying the Radon-Nikodym property are then given in terms of the agreement of dual functors of the functors mentioned above.

MSC classification

Secondary: 46M15: Categories, functors
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 4 , June 1979 , pp. 479 - 494
Copyright
Copyright © Australian Mathematical Society 1979

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