Estimates for norms of resolvents and an application to the perturbation of spectra

Abstract

Abstract Let A belong to the Schatten‐von Neumann ideal S p for 0 < p < ∞. We give an upper bound for the operator norm of the resolvent ( zI – A ) –1 of A in terms of the departure from normality of A and the distance of z to the spectrum of A . As an application we provide an upper bound for the Hausdorff distance of the spectra of two operators belonging to S p . (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)