Relatively bounded perturbations of J-non-negative operators

2019/03/10 by Friedrich Philipp, Philipp, Friedrich
Mathematics · Computer Science · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Matrix Theory and Algorithms #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1903.03977

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.

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