Spaces of Compact Operators

Access: Use of this item is restricted to the UNT Community
Description:

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.

Creator(s): Ghenciu, Ioana
Creation Date: May 2004
Partner(s):
UNT Libraries
Collection(s):
UNT Theses and Dissertations
Usage:
Total Uses: 110
Past 30 days: 7
Yesterday: 0
Creator (Author):
Publisher Info:
Publisher Name: University of North Texas
Place of Publication: Denton, Texas
Date(s):
  • Creation: May 2004
  • Digitized: November 9, 2007
Description:

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.

Degree:
Level: Doctoral
Discipline: Mathematics
Language(s):
Subject(s):
Keyword(s): compact operators | weakly compact operators | Dunford-Pettis sets
Contributor(s):
Partner:
UNT Libraries
Collection:
UNT Theses and Dissertations
Identifier:
  • OCLC: 55880600 |
  • ARK: ark:/67531/metadc4463
Resource Type: Thesis or Dissertation
Format: Text
Rights:
Access: Use restricted to UNT Community
License: Copyright
Holder: Ghenciu, Ioana
Statement: Copyright is held by the author, unless otherwise noted. All rights reserved.