Spectral properties of relatively finite-dimensional perturbations of selfadjoint operators (Q1277452)

Let \({\mathcal H}\) be an infinite-dimensional complex Hilbert space. Assume \(A\) to be a selfadjoint, semibounded operator in \({\mathcal H}\) with discrete spectrum. Let \(B\) be an operator of the form \[ Bf= \sum^N_{i=1} \langle Af,a_i\rangle b_i \] for \(f\in\text{dom}(A)\), where \(a_i\), \(b_i\) are certain vectors in \({\mathcal H}\). Then there are given estimates for the eigenvalues and eigenvectors of the perturbed operators \(A-B\).