Author Type

Graduate Student

Date of Award

2009

Document Type

Thesis

Publication Status

Version of Record

Submission Date

October 2026

Abstract

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.

Extent

v, 53 p. : ill.

Comments

by Eva, Kasprikova|Thesis (Ph.D.)--Florida Atlantic University, 2009.|Includes bibliography.|Electronic reproduction. Boca Raton, Fla., 2009. Mode of access: World Wide Web.|by Eva, Kasprikova

Identifier

FADT2684304

Format

pdf

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