Perturbation theory of commuting self-adjoint operators

Tuesday, 21 February 2023

Abstract

In this talk, I give an overview of the perturbation theory of commuting self-adjoint operators developed by Voiculescu, which generalizes the classical Weyl-von Neumann theorem and Kato-Rosenblum theorem. 

Quasicentral modulus of a tuple of operators with respect to a normed ideal plays an essential role in the theory, and we present an example of its computation in the case where the joint spectrum of the tuple is contained in a self-similar set.