Operators in Krein Space

We study self-adjoint operators in Krein space. Our goal is to show that there is a relationship between the following classes of operators: operators with a compact “corner,” definitizable operators, operators of classes (H) and K(H), and operators of class D _κ ⁺.     

On certain spectral properties of a quadratic self-adjoint matrix pencil with dominating main diagonals

Sufficient conditions for the “separation of the spectrum” of a quadratic matrix pencil with self-adjoint coefficients are found. A criterion for the representability of a positive operator in a finite-dimensional space in the form of a matrix with dominating main diagonal in each orthonormal basis is obtained. Translated fromMatematicheskie Zametki, Vol. 61, No. 3, pp. 381–390, March, 1997. Translated by A. I. Shtern