Inequalities for the eigenvalues of non-selfadjoint Jacobi operators

TL;DR

This paper establishes Lieb-Thirring-type bounds for eigenvalues of non-selfadjoint Jacobi operators, extending previous results for selfadjoint cases using advanced complex analysis and operator determinant techniques.

Contribution

It introduces new bounds for non-selfadjoint Jacobi operators, improving the strength and scope of earlier eigenvalue estimates.

Findings

Derived Lieb-Thirring-type bounds for non-selfadjoint Jacobi operators

Extended complex function theory methods to non-selfadjoint cases

Sharpened previous eigenvalue inequality results

Abstract

We prove Lieb-Thirring-type bounds on eigenvalues of non-selfadjoint Jacobi operators, which are nearly as strong as those proven previously for the case of selfadjoint operators by Hundertmark and Simon. We use a method based on determinants of operators and on complex function theory, extending and sharpening earlier work of Borichev, Golinskii and Kupin.