Probabilistic Operator Algebra Seminar: Invariance of absolutely continuous spectra under hybrid normed ideal perturbations.

Seminar | November 6 | 3:45-5:45 p.m. | 748 Evans Hall

 Dan-Virgil Voiculescu, UC Berkeley

 Department of Mathematics

In hybrid normed ideal perturbations of n-tuples of operators the normed ideal is allowed to vary with the component operator. The talk will deal with the machinery we developed for normed ideal perturbations based on a numerical invariant, the modulus of quasicentral approximation, and its extension to the hybrid setting. We used this approach to show that if two n-tuples of commuting hermitian operators differ by Lorentz (p(j) , 1) normed ideal perturbations in their j-th component and 1/p(1) + ... + 1/p(n) = 1 then their absolutely continuous parts must be unitarily equivalent. The proof involves singular integrals with mixed homogeneities.