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An eigenvalue estimate and its application to non-selfadjoint Jacobi and Schrödinger operators (1006.5308v1)
Published 28 Jun 2010 in math.SP, math-ph, and math.MP
Abstract: For bounded linear operators $A,B$ on a Hilbert space $\mathcal{H}$ we show the validity of the estimate $$ \sum_{\lambda \in \sigma_d (B)} \dist(\lambda, \overline{\num}(A))p \leq | B-A |_{\mathcal{S}_p}p$$ and apply it to recover and improve some Lieb-Thirring type inequalities for non-selfadjoint Jacobi and Schr\"odinger operators.
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