Perturbation determinants and discrete spectra of semi-infinite non-self-adjoint Jacobi operators

Leonid Golinskii

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arXiv · 2101.05562

Perturbation determinants and discrete spectra of semi-infinite non-self-adjoint Jacobi operators

Leonid Golinskii

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Abstract

We study the trace class perturbations of the half-line, discrete Laplacian and obtain a new bound for the perturbation determinant of the corresponding non-self-adjoint Jacobi operator. Based on this bound, we obtain the Lieb--Thirring inequalities for such operators. The spectral enclosure for the discrete spectrum and embedded eigenvalues are also discussed.

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Leonid Golinskii. 2021-01-14. Perturbation determinants and discrete spectra of semi-infinite non-self-adjoint Jacobi operators. https://arxiv.org/abs/2101.05562

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