Simple eigenvectors of unbounded operators of the type "normal plus compact"

The paper deals with operators of the form A = S + B, where B is a compact operator in a Hilbert space H and S is an unbounded normal one in H, having a compact resolvent. We consider approximations of the eigenvectors of A, corresponding to simple eigenvalues by the eigenvectors of the operators An = S + Bn (n = 1, 2,...), where Bn is an n-dimensional operator. In addition, we obtain the error estimate of the approximation.