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Journal of Complex Analysis
Volume 2013 (2013), Article ID 801382, 5 pages
http://dx.doi.org/10.1155/2013/801382
Research Article

Perturbations of Polynomials with Operator Coefficients

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

Received 18 December 2012; Accepted 20 February 2013

Academic Editor: Janne Heittokangas

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.

Abstract

We consider polynomials whose coefficients are operators belonging to the Schatten-von Neumann ideals of compact operators in a Hilbert space. Bounds for the spectra of perturbed pencils are established. Applications to differential and difference equations are also discussed.