Spectral Flow in Semifinite von Neumann Algebras
| dc.contributor.author | Georgescu, Magdalena Cecilia | |
| dc.contributor.supervisor | Phillips, John | |
| dc.date.accessioned | 2013-12-17T21:18:47Z | |
| dc.date.available | 2013-12-17T21:18:47Z | |
| dc.date.copyright | 2013 | en_US |
| dc.date.issued | 2013-12-17 | |
| dc.degree.department | Department of Mathematics and Statistics | |
| dc.degree.level | Doctor of Philosophy Ph.D. | en_US |
| dc.description.abstract | 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). | en_US |
| dc.description.proquestcode | 0280 | en_US |
| dc.description.scholarlevel | Graduate | en_US |
| dc.identifier.uri | http://hdl.handle.net/1828/5090 | |
| dc.language | English | eng |
| dc.language.iso | en | en_US |
| dc.rights.temp | Available to the World Wide Web | en_US |
| dc.subject | spectral flow | en_US |
| dc.subject | semifinite von Neumann algebra | en_US |
| dc.title | Spectral Flow in Semifinite von Neumann Algebras | en_US |
| dc.type | Thesis | en_US |