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Compact and Finite Rank Perturbations of Selfadjoint Operators in Krein Spaces with Applications to Boundary Eigenvalue Problems (eBook, PDF)

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A selfadjoint operator A in a Krein space (K, [•, •]) is called definitizable if the resolvent set ρ(A) is nonempty and there exists a polynomial p such that [p(A)x, x] ≥ 0 for all x ∈ dom (p(A)). It was shown in [L1] and [L5] that a definitizable operator A has a spectral function EA which is defined for all real intervals the boundary points of which do not belong to some finite subset of the real axis. With the help of the spectral function the real points of the spectrum σ(A) of A can be classified in...

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