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.
Full Text
Article Information
| Title | Properties of the spectrum of type $\pi_{+}$ and type $\pi_{-}$ of self-adjoint operators in Krein spaces |
| Source | Methods Funct. Anal. Topology, Vol. 12 (2006), no. 4, 326-340 |
| MathSciNet |
MR2279870 |
| Copyright | The 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
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},
MRNUMBER = {MR2279870},
URL = {http://mfat.imath.kiev.ua/article/?id=362},
}
