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

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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*. ... continued below

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iii, 43 leaves

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Leavelle, Tommy L. (Tommy Lee) August 1984.

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  • Leavelle, Tommy L. (Tommy Lee)

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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.

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iii, 43 leaves

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  • August 1984

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  • Aug. 22, 2014, 6 p.m.

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  • Jan. 22, 2018, 9:46 a.m.

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Leavelle, Tommy L. (Tommy Lee). The Reciprocal Dunford-Pettis and Radon-Nikodym Properties in Banach Spaces, dissertation, August 1984; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc331441/: accessed February 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .