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

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.

Spectral enclosures and stability for non‐self‐adjoint discrete Schrödinger operators on the half‐line

“…The case of discrete Dirac operators on ℤ was investigated in [4]. Except for these studies and few more relevant papers such as [9,10,14], we are not aware of more works on discrete counterparts of the (comparatively many) differential settings studied in the last two decades.…”