Doctor of Philosophy
School of Mathematics and Applied Statistics
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
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.