Eigenvalues of a certain quadratic pencil of operators
In a separable Hilbert space the quadratic pencil \[ L(\lambda)=\lambda^ 2I+\lambda (\alpha A+C)+A \] is considered. Here A and C are closed linear operators, \(A\geq -\beta /2I\) \((\beta >0)\), \(\alpha\geq 0\), and the negative part of the spectrum of A is discrete. It is assumed also that \(C\geq 0\) is symmetric and is A-bounded in the sense of Kato. It is stated that the number of eigenvalues of L(\(\lambda)\) with positive real part is equal to the number of negative eigenvalues of A.
number of eigenvalues with positive real part
scientific article; zbMATH DE number 4109411