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Eigenvalue bounds in the gaps of Schrödinger operators and Jacobi matrices. (English) Zbl 1135.47026
Let $$A$$ be a selfadjoint operator and $$(x,y)$$ be a gap in its spectrum. The main result of the paper provides a bound for the number of eigenvalues of the operator $$C=A+B$$, $$B=B_+-B_-$$ with $$B_{\pm1}\geq 0$$ and both compact, inside $$(x,y)$$. As an application, the Lieb–Thirring-type bounds for the eigenvalues of the Jacobi matrices $$J=J_0+\delta J$$, which are trace class perturbations of algebro-geometric almost periodic Jacobi matrices, are obtained.

##### MSC:
 47B36 Jacobi (tridiagonal) operators (matrices) and generalizations 47A55 Perturbation theory of linear operators
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##### References:
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