Hari Bercovici - Norm ideal perturbations of commuting self-adjoint operators

Given an n-tuple of commuting self-adjoint operators, and an ideal J of compact operators, one is interested in the existence of an n-tuple such that T+K is diagonal in some orthonormal basis. When such an n-tuple K does not exist then we say that J is an obstruction ideal (for the diagonalization of T). We will discuss some cases when Lorentz ideals are obstruction ideals. We will also consider the perturbation problems which arise when T is replaced by an infinite family. Some of Voiculescu's characterizations of obstruction ideals (involving, e.g., quasicentral approximate units) can be extended to cover such families.