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

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Abstract

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