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

TL;DR

This paper investigates the spectral properties of non-self-adjoint Jacobi operators on the half-line, deriving new bounds for perturbation determinants, establishing Lieb-Thirring inequalities, and analyzing the discrete spectrum and embedded eigenvalues.

Contribution

It introduces a novel bound for the perturbation determinant of non-self-adjoint Jacobi operators and applies it to derive Lieb-Thirring inequalities and spectral enclosures.

Findings

New bound for the perturbation determinant of non-self-adjoint Jacobi operators

Lieb-Thirring inequalities established for these operators

Spectral enclosure results for discrete spectrum and embedded eigenvalues

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.