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arXiv · 1006.5308

An eigenvalue estimate and its application to non-selfadjoint Jacobi and Schrödinger operators

Marcel Hansmann
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Abstract

For bounded linear operators $A,B$ on a Hilbert space $\mathcal{H}$ we show the validity of the estimate $$ \sum_{λ\in σ_d (B)} \dist(λ, \overline{\num}(A))^p \leq \| B-A \|_{\mathcal{S}_p}^p$$ and apply it to recover and improve some Lieb-Thirring type inequalities for non-selfadjoint Jacobi and Schrödinger operators.

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Marcel Hansmann. 2010-06-28. An eigenvalue estimate and its application to non-selfadjoint Jacobi and Schrödinger operators. https://doi.org/10.1007/s11005-011-0494-9

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