On the Spectral Theory of Operator Pencils in a Hilbert Space

DOI

10.2991/jnmp.1995.2.3-4.15How to use a DOI?

Abstract

Consider the operator pencil L = A - B - 2 C, where A, B, and C are linear, in general unbounded and nonsymmetric, operators densely defined in a Hilbert space H. Sufficient conditions for the existence of the eigenvalues of L are investigated in the case when A, B and C are K-positive and K-symmetric operators in H, and a method to bracket the eigenvalues of L is developed by using a variational characterization of the problem (i) Lu = 0. The method generates a sequence of lower and upper bounds converging to the eigenvalues of L and can be considered an extension of the Temple-Lehman method to quadratic eigenvalue problems (i).

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Roman I. Andrushkiw
PY  - 1995
DA  - 1995/09/01
TI  - On the Spectral Theory of Operator Pencils in a Hilbert Space
JO  - Journal of Nonlinear Mathematical Physics
SP  - 356
EP  - 366
VL  - 2
IS  - 3-4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1995.2.3-4.15
DO  - 10.2991/jnmp.1995.2.3-4.15
ID  - Andrushkiw1995
ER  -