An eigenvalue estimate and its application to non-selfadjoint Jacobi and Schr\"odinger operators

Marcel Hansmann

doi:10.1007/s11005-011-0494-9

An eigenvalue estimate and its application to non-selfadjoint Jacobi and Schr\"odinger operators

Spectral Theory 2011-09-20 v1 Mathematical Physics math.MP

Authors: 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 $\sum_{\lambda \in \sigma_d (B)} \dist(\lambda, \overline{\num}(A))^p \leq \| B-A \|_{\mathcal{S}_p}^p$ and apply it to recover and improve some Lieb-Thirring type inequalities for non-selfadjoint Jacobi and Schr\"odinger operators.

Keywords

operator theory and elliptic operators magnetic schrödinger operator operator theory on hilbert spaces

Cite

@article{arxiv.1006.5308,
  title  = {An eigenvalue estimate and its application to non-selfadjoint Jacobi and Schr\"odinger operators},
  author = {Marcel Hansmann},
  journal= {arXiv preprint arXiv:1006.5308},
  year   = {2011}
}

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