On a conjecture by Hundertmark and Simon

• Main Authors: Ari Laptev, Michael Loss, Lukas Schimmer
• Format: Article in Journal/Newspaper
• Language: unknown
• Published: 2022
• Subjects: Mathematical physics; Physical sciences; Nuclear and plasma physics; Particle and high energy physics; Science & Technology; Physics; Multidisciplinary; Particles & Fields; Mathematical; laptev
• Online Access: https://figshare.com/articles/journal_contribution/On_a_conjecture_by_Hundertmark_and_Simon/24591981

The main result of this paper is a complete proof of a new Lieb–Thirring-type inequality for Jacobi matrices originally conjectured by Hundertmark and Simon. In particular, it is proved that the estimate on the sum of eigenvalues does not depend on the off-diagonal terms as long as they are smaller than their asymptotic value. 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. This technique seems to be novel in the context of Jacobi matrices.