A remark on a paper by Hundertmark and Simon

TL;DR

This paper proves a sharp Lieb-Thirring inequality for Jacobi matrices, confirming a conjecture by Hundertmark and Simon, and introduces a novel proof technique involving sums of singular values for compact operators.

Contribution

It establishes a new sharp inequality for Jacobi matrices and employs a unique proof method based on singular value sums, advancing spectral theory.

Findings

Proved a sharp Lieb-Thirring inequality for Jacobi matrices

Confirmed a conjecture of Hundertmark and Simon

Introduced a novel proof technique involving sums of singular values

Abstract

We prove a sharp Lieb-Thirring type inequality for Jacobi matrices, thereby settling a conjecture of Hundertmark and Simon. An interesting feature of the proof is that it employs a technique originally used by Hundertmark-Laptev-Weidl concerning sums of singular values for compact operators.