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

Heinz Langer, Matthias Langer, Alexander Markus, Christiane Tretter

Research output: Contribution to journalArticle

8 Citations (Scopus)

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.
LanguageEnglish
Pages115-136
Number of pages22
JournalLinear and Multilinear Algebra
Volume53
Issue number2
DOIs
Publication statusPublished - 2005

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Krein Space
Self-adjoint Operator
Interval
Operator
Subspace
Schur Complement
Spectral Function
Variational Principle
Defects
Eigenvalue

Keywords

  • Krein space
  • spectrum of definite type
  • local spectral function
  • quadratic numerical range
  • variational principle for eigenvalues

Cite this

Langer, Heinz ; Langer, Matthias ; Markus, Alexander ; Tretter, Christiane. / Spectrum of definite type of self-adjoint operators in Krein spaces. In: Linear and Multilinear Algebra. 2005 ; Vol. 53, No. 2. pp. 115-136.
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Spectrum of definite type of self-adjoint operators in Krein spaces. / Langer, Heinz; Langer, Matthias; Markus, Alexander; Tretter, Christiane.

In: Linear and Multilinear Algebra, Vol. 53, No. 2, 2005, p. 115-136.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Spectrum of definite type of self-adjoint operators in Krein spaces

AU - Langer, Heinz

AU - Langer, Matthias

AU - Markus, Alexander

AU - Tretter, Christiane

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

KW - Krein space

KW - spectrum of definite type

KW - local spectral function

KW - quadratic numerical range

KW - variational principle for eigenvalues

U2 - 10.1080/03081080500055049

DO - 10.1080/03081080500055049

M3 - Article

VL - 53

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EP - 136

JO - Linear and Multilinear Algebra

T2 - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

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ER -