On a conjecture by Hundertmark and Simon
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...
Main Authors: | , , |
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Format: | Article in Journal/Newspaper |
Language: | unknown |
Published: |
2022
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Subjects: | |
Online Access: | https://figshare.com/articles/journal_contribution/On_a_conjecture_by_Hundertmark_and_Simon/24591981 |
Summary: | 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. |
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