# Relatively bounded perturbations of J-non-negative operators

## TL;DR

This paper advances perturbation theory for J-non-negative operators, providing improved spectral bounds and applying these results to indefinite Sturm-Liouville problems with L^p potentials.

## Contribution

It introduces new perturbation results for J-non-negative operators and spectral enclosures for diagonally dominant J-self-adjoint matrices.

## Key findings

- Enhanced bounds on non-real eigenvalues of indefinite Sturm-Liouville operators
- Spectral enclosures for diagonally dominant J-self-adjoint matrices
- Improved perturbation theorems for 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.