In 2002, Hundertmark and Simon proved Lieb–Thirring inequalities for Jacobi operators. They conjectured that their bounds could be improved by replacing a term (which depends on the off-diagonal parts of the operator) by its positive part. In this talk, I will present a proof of their conjecture. Subsequently I will relate (sharp) Lieb–Thirring inequalities for Jacobi operators to (sharp) Lieb–Thirring inequalities for Schrödinger operators on the real line.

This talk is partly based on joint work with A. Laptev and M. Loss.

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