A remark on the discrete spectrum of non-self-adjoint Jacobi operators

DOI10.1007/S00020-021-02679-9zbMATH Open1508.47070arXiv2101.01974MaRDI QIDQ6357700

Publication date: 6 January 2021

Abstract: We study the trace class perturbations of the whole-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 refine the Lieb--Thirring inequality due to Hansmann--Katriel. The spectral enclosure for such operators is also discussed.

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Eigenvalue problems for linear operators (47A75) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36) Nonselfadjoint operators (47B28)

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