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

DOI10.4171/JST/420arXiv2101.05562MaRDI QIDQ6358277

Publication date: 14 January 2021

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.

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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