Probabilistic Operator Algebra Seminar: Matrix-valued measures in perturbation theory

Seminar | April 22 | 2-4 p.m. | 736 Evans Hall

 Constanze Liaw, University of Delaware and CASPER at Baylor University

 Department of Mathematics

The Aronszajn-Donoghue theorem provides a good understanding of the subtle theory of rank one perturbations. One of their statements consists of the mutual singularity of the singular parts of the spectral measures under rank one perturbations. For higher rank perturbations, simple examples show that the singular parts can behave more complicatedly. Nonetheless, a 'vector' version of the mutual singularity of the singular parts and a modified Aleksandrov spectral averaging prevail in the finite rank setting. Applications of these results yield further restrictions of the singular spectrum under finite rank perturbations. The presentation is based on joint work with Sergei Treil.