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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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