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

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

2010-06-28

arxiv.org/abs/1006.5308v1

Lett. Math. Phys. (2011) 98: 79-95

Mathematics

Spectral Theory

Scientific paper

10.1007/s11005-011-0494-9

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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