On General Cwikel–Lieb–Rozenblum and Lieb–Thirring Inequalities

@article{Molchanov2008OnGC,
  title={On General Cwikel–Lieb–Rozenblum and Lieb–Thirring Inequalities},
  author={Stanislav Molchanov and Boris Vainberg},
  journal={arXiv: Mathematical Physics},
  year={2008},
  pages={201-246},
  url={https://api.semanticscholar.org/CorpusID:15416434}
}
These classical inequalities allow one to estimate the number of negative eigenvalues and the sums \(S_\gamma = \sum { |\lambda _i |^\gamma } \) for a wide class of Schrodinger operators. We provide a detailed proof of these inequalities for operators on functions in metric spaces using the classical Lieb approach based on the Kac–Feynman formula. The main goal of the paper is a new set of examples which include perturbations of the Anderson operator, operators on free, nilpotent, and solvable… 
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