You are here

FAU Collections » FAU Research Repository » FAU Theses and Dissertations

Higher order commutators in the method of orbits

Download pdf | Full Screen View

Date Issued:
2009
Summary:
Benson spaces of higher order are introduced extending the idea of N. Krugljak and M. Milman, A distance between orbits that controls commutator estimates and invertibilty of operators, Advances in Mathematics 182 (2004), 78-123. The concept of Benson shift operators is introduced and a class of spaces equipped with these operators is considered. Commutator theorems of higher order on orbit spaces generated by a single element are proved for this class. It is shown that these results apply to the complex method of interpolation and to the real method of interpolation for the case q=1. Two new characterizations are presented of the domain space of the "derivation" operator in the context of orbital methods. Comparisons to the work of others are made, especially the unifying paper of M. Cwikel, N. Kalton, M. Milman and R. Rochberg, A United Theory of Commutator Estimates for a Class of Interpolation Methods, Advances in Mathematics 169 2002, 241-312.
Title: Higher order commutators in the method of orbits.
143 views
35 downloads
Name(s): Kasprikova, Eva.
Charles E. Schmidt College of Science
Department of Mathematical Sciences
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Date Issued: 2009
Publisher: Florida Atlantic University
Physical Form: electronic
Extent: v, 53 p. : ill.
Language(s): English
Summary: Benson spaces of higher order are introduced extending the idea of N. Krugljak and M. Milman, A distance between orbits that controls commutator estimates and invertibilty of operators, Advances in Mathematics 182 (2004), 78-123. The concept of Benson shift operators is introduced and a class of spaces equipped with these operators is considered. Commutator theorems of higher order on orbit spaces generated by a single element are proved for this class. It is shown that these results apply to the complex method of interpolation and to the real method of interpolation for the case q=1. Two new characterizations are presented of the domain space of the "derivation" operator in the context of orbital methods. Comparisons to the work of others are made, especially the unifying paper of M. Cwikel, N. Kalton, M. Milman and R. Rochberg, A United Theory of Commutator Estimates for a Class of Interpolation Methods, Advances in Mathematics 169 2002, 241-312.
Identifier: 653112182 (oclc), 2684304 (digitool), FADT2684304 (IID), fau:3514 (fedora)
Note(s): by Eva, Kasprikova
Thesis (Ph.D.)--Florida Atlantic University, 2009.
Includes bibliography.
Electronic reproduction. Boca Raton, Fla., 2009. Mode of access: World Wide Web.
Subject(s): Operator theory
Interpolation spaces
Finite groups
Sporadic groups (Mathematics)
Persistent Link to This Record: http://purl.flvc.org/FAU/2684304
Use and Reproduction: http://rightsstatements.org/vocab/InC/1.0/
Host Institution: FAU