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https://hdl.handle.net/2142/68169
Description
Title
Dunford-Pettis Sets and Operators
Author(s)
Andrews, Kevin Thomas
Issue Date
1980
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
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.
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