Speaker: Hanne Schultz
Affiliation: University of Southern Denmark
Title: The Invariant Subspace Problem Relative to a Factor of Type II_1
Time and Place: Friday, 10/21, 4:05-5:00pm, Milner 317
Abstract: The invariant subspace problem relative to a von Neumann algebra M asks: For every operator T in M, does there exist a non-trivial projection P in M such that PTP=TP? This problem remains open for all infinite-dimensional factors. However, in the case of a factor M of type II_1, we have shown that if the Brown measure of T is not a Dirac measure, then there is a non-trivial projection P in W*(T) such that PTP=TP. This is a consequence of a nice result on spectral subspaces of operators in M which will be the main topic of our talk. We give an outline of the proof and discuss some applications.