The Reciprocal Dunford-Pettis and Radon-Nikodym Properties in Banach Spaces

In this paper we give a characterization theorem for the reciprocal Dunford-Pettis property as defined by Grothendieck. The relationship of this property to Pelczynski's property V is examined. In particular it is shown that every Banach space with property V has the reciprocal Dunford-Pettis p...

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Bibliographic Details
Main Author Leavelle, Tommy L. (Tommy Lee)
Format Dissertation
LanguageEnglish
Published North Texas State University 01.08.1984
Subjects
Banach spaces
Dunford-Pettis properties
Radon-Nikodym properties
Radon-Nikodym property
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Summary:In this paper we give a characterization theorem for the reciprocal Dunford-Pettis property as defined by Grothendieck. The relationship of this property to Pelczynski's property V is examined. In particular it is shown that every Banach space with property V has the reciprocal Dunford-Pettis property and an example is given to show that the converse fails to hold. Moreover the characterizations of property V and the reciprocal Dunford-Pettis property lead to the definitions of property V* and property RDP* respectively. Me compare and contrast results for the reciprocal Dunford-Pettis property and property RDP* with those for properties V and V*. In the final chapter we use a result of Brooks to obtain a characterization for the Radon-Nikodým property.