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

Let A be a self-adjoint operator, let (α, β) be a gap in the spectrum of A, and let B = A + V, where, in general, the perturbation operator V is unbounded. We establish some abstract conditions under which the spectrum of B in (α, β) is discrete; does not accumulate to β; is finite. An estimate of the number of eigenvalues of B in (α, β) is obtained. © 2000 Kluwer Academic/Plenum Publishers.