Degree Name

Doctor of Philosophy


School of Mathematics and Applied Statistics


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



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