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.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc331441 |
| Date | 08 1900 |
| Creators | Leavelle, Tommy L. (Tommy Lee) |
| Contributors | Lewis, Paul Weldon, Bilyeu, Russell Gene, Neuberger, John W., Dawson, David Fleming |
| Publisher | North Texas State University |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iii, 43 leaves, Text |
| Rights | Public, Leavelle, Tommy L. (Tommy Lee), Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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