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Properties of the spectrum of type $\pi_{+}$ and type $\pi_{-}$ of self-adjoint operators in Krein spaces


Abstract

We investigate spectral points of type $\pi_{+}$ and type $\pi_{-}$ for self-adjoint operators in Krein spaces. In particular a sharp lower bound for the codimension of the linear manifold $H_0$ occuring in the definition of spectral points of type $\pi_+$ and type $\pi_-$ is determined. Furthermore, we describe the structure of the spectrum in a small neighbourhood of such points and we construct a finite dimensional perturbation which turns a real spectral point of type $\pi_{+}$ (type $\pi_{-}$) into a point of positive (resp.\ negative) type. As an application we study a singular Sturm-Liouville operator with an indefinite weight.


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Article Information

TitleProperties of the spectrum of type $\pi_{+}$ and type $\pi_{-}$ of self-adjoint operators in Krein spaces
SourceMethods Funct. Anal. Topology, Vol. 12 (2006), no. 4, 326-340
MathSciNet MR2279870
CopyrightThe Author(s) 2006 (CC BY-SA)

Authors Information

Jussi Behrndt
Technische Universitat Berlin, Institut fur Mathematik MA 6--4, Strasse des 17. Juni 136, D-10623 Berlin

Friedrich Philipp
Technische Universitat Berlin, Institut fur Mathematik MA 6--4, Strasse des 17. Juni 136, D-10623 Berlin

Carsten Trunk
Technische Universitat Berlin, Institut fur Mathematik MA 6--4, Strasse des 17. Juni 136, D-10623 Berlin


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Citation Example

Jussi Behrndt, Friedrich Philipp, and Carsten Trunk, Properties of the spectrum of type $\pi_{+}$ and type $\pi_{-}$ of self-adjoint operators in Krein spaces, Methods Funct. Anal. Topology 12 (2006), no. 4, 326-340.


BibTex

@article {MFAT362,
    AUTHOR = {Behrndt, Jussi and Philipp, Friedrich and Trunk, Carsten},
     TITLE = {Properties of the spectrum of type $\pi_{+}$ and type $\pi_{-}$ of self-adjoint operators in Krein spaces},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {12},
      YEAR = {2006},
    NUMBER = {4},
     PAGES = {326-340},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=362},
}


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