Analysis seminar

Magdalena Georgescu, University of Victoria

"Characterization of spectral flow in a type II factor"

In B(H) (the set of bounded operators on a Hilbert space), the spectral flow counts the net number of eigenvalues which change sign as one travels along a path of self-adjoint Fredholm operators. The ability to calculate the spectral flow allows one to calculate the Fredholm index of some operators, making it of interest in the study of noncommutative geometry. It is possible to generalize the concept of spectal flow to a semifinite von Neumann algebra, as we can use a trace on the algebra to measure the amount of spectrum which changes sign.
Lesch showed in the type I case (i.e. B(H)) that a map on a suitable set of paths which satisfies three fairly straight-forward conditions is the spectral flow map. In this talk, I will describe how Lesch's ideas can be modified to obtain a characterization of spectral flow in a type II factor.