Alexander Müller-Hermes, Technical University Munich, Germany

Spectral variation bounds via finite Blaschke products

Abstract

We derive new estimates for distances between optimal matchings of eigenvalues of non-normal matrices in terms of the norm of their difference. We introduce and estimate a hyperbolic metric analogue of the classical spectral variation distance. Our apporach is based on the theory of model operators, which provides strong resolvent estimates. The latter naturally lead to a Chebychev-type interpolation problem with finite Blaschke products, which can be solved explicitly. Our bound improves on the best known classical spectral variation bounds if the distance of matrices is sufficiently small and it is sharp for asymptotically large matrices.