Special Session 164: Periodic and Ergodic Schrodinger Operators

Singular Spectrum under a Wide Class of Perturbations
Constanze D Liaw
University of Delaware
USA
Co-Author(s):    Eero Saksman, Sergei Treil
Abstract:
For bounded self-adjoint operators $A$ and $K$ on a separable Hilbert space, consider perturbed operators of the form $A+K$. We present restrictions on the singular spectrum under trace class and more general perturbations. Some of the results are for a one-parameter family of perturbations $A+tK$, as the real parameter $t$ varies. To the best of our knowledge, these are the first statements on the singular spectrum under infinite rank perturbations.