Spaces of Compact Operators

In this dissertation we study the structure of spaces of operators, especially the space of all compact operators between two Banach spaces X and Y. Work by Kalton, Emmanuele, Bator and Lewis on the space of compact and weakly compact operators motivates much of this paper. Let L(X,Y) be the Banach space of all bounded linear operators between Banach spaces X and Y, K(X,Y) be the space of all compact operators, and W(X,Y) be the space of all weakly compact operators. We study problems related to the complementability of different operator ideals (the Banach space of all compact, weakly compact, completely continuous, resp. unconditionally converging) operators in the space of all bounded linear operators. The structure of Dunford-Pettis sets, strong Dunford-Pettis sets, and certain spaces of operators is studied in the context of the injective and projective tensor products of Banach spaces. Bibasic sequences are used to study relative norm compactness of strong Dunford-Pettis sets. Next, we use Dunford-Pettis sets to give sufficient conditions for K(X,Y) to contain c0.

Grantor dc:publisher

University of North Texas

Year dc:date

2004

Author dc:creator

• Ghenciu, Ioana

Contributors dc:contributor

• Lewis, Paul
• Bator, Elizabeth M.
• Brand, Neal

• Compact operators.
• Banach spaces -- Dunford-Pettis properties.
• bibasic sequences
• Dunford-Pettis sets
• weakly compact operators
• operator ideals

Statement dc:rights

• Use restricted to UNT Community
• Copyright
• Ghenciu, Ioana
• Copyright is held by the author, unless otherwise noted. All rights reserved.

Language dc:language

English

Identifier

oclc: 55880600
https://digital.library.unt.edu/ark:/67531/metadc4463/
ark: ark:/67531/metadc4463

OAI identifier oai:identifier

info:ark/67531/metadc4463