H. Langer, M. Langer, A. Markus and C. Tretter,
Spectrum of definite type of self-adjoint operators in Krein spaces,
Linear and Multilinear Algebra 53 (2005), 115–136

Abstract:
For a self-adjoint operator in a Krein space we construct an interval [ν,μ] outside of which the operator has only a spectrum of definite type and possesses a local spectral function. As a consequence, a spectral subspace corresponding to an interval outside [ν,μ] admits an angular operator representation. We describe a defect subspace of the domain of the angular operator in terms of the Schur complement, and we derive variational principles for the discrete eigenvalues in such intervals of definite type.

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