Table of Contents
International Journal of Analysis
Volume 2013, Article ID 243891, 4 pages
Research Article

A New Identity for Resolvents of Operators

Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, 84105 Beer-Sheva, Israel

Received 10 December 2012; Accepted 21 December 2012

Academic Editor: Jens Lorenz

Copyright © 2013 Michael Gil'. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new identity for resolvents of operators is suggested. We show that in appropriate situations it is more convenient than the Hilbert identity. In particular, we establish a new invertibility condition for perturbed operators as well as new bounds for the spectrum of perturbed operators. As a particular case we consider perturbations of Hilbert-Schmidt operators.