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IMCS/Publications/BASM/Issues/BASM n.1 (7), 1992/

On the spectrum in the right half-plane of a class of operator pencils. (Russian)

Authors: Barkari S. M., Pivovarchik V. N.

Abstract

The operator pensil $L(\lambda, \eta)=\lambda^2(I-P)+ \lambda \eta (iB+C)+A$ which works in Hilbert separable space is considered. It was proved that total algebraic multiple of spectrum $L(\lambda, \eta)$ in open right semi-plane does not depend on $\eta \in [0,1]$, while some natural conditions are putted on $A$, $B$, $C$ and $P$.