## Year

2015

## Degree Name

Doctor of Philosophy

## Department

School of Mathematics and Applied Statistics

## Recommended Citation

Andersson, Andreas, The noncommutative Gohberg-Krein theorem, Doctor of Philosophy thesis, School of Mathematics and Applied Statistics, University of Wollongong, 2015. https://ro.uow.edu.au/theses/4565

## Abstract

We prove a noncommutative higher-dimensional generalization of the classical Gohberg- Krein theorem. The latter says that the index of a Toeplitz operator acting on Hardy space is equal to minus the winding number of its symbol (a function on the circle). In the process we construct an explicit realization of the KK Thom class in terms of a Dirac operator.

## FoR codes (2008)

010103 Category Theory, K Theory, Homological Algebra, 010108 Operator Algebras and Functional Analysis, 010199 Pure Mathematics not elsewhere classified, 010501 Algebraic Structures in Mathematical Physics

**Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.**