Relatively Bounded Perturbations of J-Non-Negative Operators

Abstract

We improve known perturbation results for self-adjoint operators in Hilbert spaces and prove spectral enclosures for diagonally dominant J-self-adjoint operator matrices. These are used in the proof of the central result, a perturbation theorem for J-non-negative operators. The results are applied to singular indefinite Sturm-Liouville operators with L^p-potentials. Known bounds on the non-real eigenvalues of such operators are improved.