Discrete spectrum in spectral gaps of a self-adjoint operator under unbounded perturbations (Q1588949)

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scientific article; zbMATH DE number 1541240
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Discrete spectrum in spectral gaps of a self-adjoint operator under unbounded perturbations
scientific article; zbMATH DE number 1541240

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    Discrete spectrum in spectral gaps of a self-adjoint operator under unbounded perturbations (English)
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    11 December 2000
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    For a self-adjoint operator \(A\) in a Hilbert space \(V\), let \(B\) be its perturbation; \(B= A+ V\), where \(V\) may be unbounded. Let the spectrum of \(A\) contain a gap \((\alpha, \beta)\). The author obtains abstract conditions under which the spectrum of \(B\) is discrete, is finite and does not accumulate to \(\beta\). An estimate for the number of eigenvalues of \(B\) in \((\alpha, \beta)\) is also obtained.
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    self-adjoint operator
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    perturbation
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    spectrum
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    number of eigenvalues
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