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

✍ Scribed by Oscar F. Bandtlow

• Publisher: John Wiley and Sons
• Year: 2004
• Tongue: English
• Weight: 517 KB
• Volume: 267
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200310149

✦ Synopsis

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)