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

Heinz Langer, Matthias Langer, Alexander Markus, Christiane Tretter

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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.

Original languageEnglish
Pages (from-to)115-136
Number of pages22
JournalLinear and Multilinear Algebra
Volume53
Issue number2
DOIs
StatePublished - 1 Mar 2005

Keywords

  • Krein space
  • Local spectral function
  • Quadratic numerical range
  • Spectrum of definite type
  • Variational principle for eigenvalues

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