Spectral flow, in its simplest incarnation, counts the net number of eigenvalues which change sign as one traverses a path of self-adjoint Fredholm operators in the set of of bounded operators B(H) on a Hilbert space. A generalization of this idea changes the setting to a semifinite von Neumann algebra N and uses the trace τ to measure the amount of spectrum which changes from negative to positive along a path; the operators are still self-adjoint, but the Fredholm requirement is replaced by its von Neumann algebras counterpart, Breuer-Fredholm.
Our work is ensconced in this semifinite von Neumann algebra setting. We prove a uniqueness result in the case when N is a factor. In the case when the operators under consideration are bounded perturbations of a fixed unbounded operator with τ-compact resolvents, we give a different proof of a p-summable integral formula which calculates spectral flow, and fill in some of the gaps in the proof that spectral flow can be viewed as an intersection number if N = B(H). / Graduate / 0280
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/5090 |
| Date | 17 December 2013 |
| Creators | Georgescu, Magdalena Cecilia |
| Contributors | Phillips, John |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web |
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