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Open Access research with a European policy impact...

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EPRC is a leading institute in Europe for comparative research on public policy, with a particular focus on regional development policies. Spanning 30 European countries, EPRC research programmes have a strong emphasis on applied research and knowledge exchange, including the provision of policy advice to EU institutions and national and sub-national government authorities throughout Europe.

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Spectrum of definite type of self-adjoint operators in Krein spaces

Langer, Heinz and Langer, Matthias and Markus, Alexander and Tretter, Christiane (2005) Spectrum of definite type of self-adjoint operators in Krein spaces. Linear and Multilinear Algebra, 53 (2). pp. 115-136. ISSN 0308-1087

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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.