Abstract
dc:descriptionSets 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.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2014
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Andrews, Kevin Thomas
Subjects
dc:subject × 1Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- (UMI)AAI8026446
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/68169