Perturbações unitárias multiplicativas

Abstract

For the self-adjoint operator H, the perturbation H+A, with A also a self-adjoint operator, there is a long list of results regarding the spectrum of this perturbation. We study the spectrum of a multiplicative perturbation XU (UX) with U and X unitary operators. Specifically, we find similar results for the Howland, Weyl-von Neumann Theorems and the continuous singular spectrum for a perturbation of rank one.