Lipschitz and commutator estimates, a unified approach.

Author: Denis Potapov

Potapov, Denis, 2007 Lipschitz and commutator estimates, a unified approach., Flinders University, School of Informatics and Engineering

This electronic version is made publicly available by Flinders University in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. This thesis may incorporate third party material which has been used by the author pursuant to Fair Dealing exceptions. If you are the owner of any included third party copyright material and/or you believe that any material has been made available without permission of the copyright owner please contact with the details.


The subject of the thesis is the study of operator functions in the setting of symmetric operator spaces. In this latter setting, it is of great importance to analyze the properties of so-called operator functions A --> f(A), where the variable A is a self-adjoint operator and f is a complex-valued Borel function on the real line. The thesis study the question of differentiability of this type of operator functions. The latter question is intimately related to the study of commutators. Text not only extends existing results to the setting of unbounded self-adjoint linear operators, but it is also shown that this can be obtained via a unified approach utilizing the left regular representation of von Neumann algebras.

Keywords: Lipschitz estimates,commutator estimates,symmetric noncommutative spaces

Subject: Mathematics thesis

Thesis type: Doctor of Philosophy
Completed: 2007
School: School of Computer Science, Engineering and Mathematics
Supervisor: Dr. Fyodor Sukochev