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Title:Dunford-Pettis Sets and Operators
Author(s):Andrews, Kevin Thomas
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract:Sets in Banach spaces that are mapped into norm compact sets by weakly compact operators (called Dunford-Pettis sets) are studied in general and in the spaces L(,1) ((mu),X), C((OMEGA),X), and P(,1)((mu),X). It is shown that if X is a Banach space with the Dunford-Pettis property and X contains no copy (,1), then L(,1)((mu),X) has the Dunford-Pettis property. Furthermore, if X has the Dunford-Pettis property and M is a subset of L(,1)((mu),X) that satisfies any of the extant criteria for weak compactness in L(,1)((mu),X), then it is shown that M is a Dunford-Pettis set. Various classes of Dunford-Pettis operators on L(,1) ((mu),X) are examined from the point of view of measurability properties of representing kernels. The relationship between structural properties of operators on C((OMEGA),X) and L(,(INFIN))((mu),X*) and properties of their representing measures is explored.
Issue Date:1980
Type:Text
Language:English
Description:113 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1980.
URI:http://hdl.handle.net/2142/68169
Other Identifier(s):(UMI)AAI8026446
Date Available in IDEALS:2014-12-14
Date Deposited:1980


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