F. Philipp

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Articles: 1

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

Jussi Behrndt, Friedrich Philipp, Carsten Trunk

MFAT 12 (2006), no. 4, 326-340

326-340

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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