Event Title
Schur-type decompositions in II-1 factors
Location
Crow 206
Start Date
7-22-2016 5:30 PM
End Date
22-7-2016 5:50 PM
Description
Brown measure is a sort of spectral distribution for arbitrary operators (including non-selfadjoint ones) in II_1-factors. Haagerup and Schultz proved existence of hyperinvariant projections for operators in II_1-factors, that split the operator according to the Brown measure. With Sukochev and Zanin, we used these to prove a sort of upper trianguler decomposition result for such elements, analogous to Schur's famous result for matrices. More recently, we have partially extended these results to certain unbounded operators affiliated with II_1-factors. One application is to show that every trace is spectral (i.e., the value of the trace depends only on the Brown measure of the operator) for traces on certain bimodules of affiliated operators (these are often called Dixmier traces). Time permitting, we will mention some results about the nature of the spectrally trivial parts in these upper triangular forms.
Schur-type decompositions in II-1 factors
Crow 206
Brown measure is a sort of spectral distribution for arbitrary operators (including non-selfadjoint ones) in II_1-factors. Haagerup and Schultz proved existence of hyperinvariant projections for operators in II_1-factors, that split the operator according to the Brown measure. With Sukochev and Zanin, we used these to prove a sort of upper trianguler decomposition result for such elements, analogous to Schur's famous result for matrices. More recently, we have partially extended these results to certain unbounded operators affiliated with II_1-factors. One application is to show that every trace is spectral (i.e., the value of the trace depends only on the Brown measure of the operator) for traces on certain bimodules of affiliated operators (these are often called Dixmier traces). Time permitting, we will mention some results about the nature of the spectrally trivial parts in these upper triangular forms.