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Spectral Flow in Semifinite von Neumann AlgebrasGeorgescu, Magdalena Cecilia 17 December 2013 (has links)
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
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