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.
Original language | English |
---|---|
Pages (from-to) | 115-136 |
Number of pages | 22 |
Journal | Linear and Multilinear Algebra |
Volume | 53 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2005 |
Keywords
- Krein space
- spectrum of definite type
- local spectral function
- quadratic numerical range
- variational principle for eigenvalues