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