On the point spectrum of H-2-singular perturbations

We prove that for any self-adjoint operator A in a separable Hilbert space H and a given countable set Lambda={lambda(i)}(i is an element of N) of real numbers, there exist H-2-singular perturbations (A) over tilde of A such that Lambda subset of sigma(p) ((A) over tilde). In particular, if Lambda={lambda(1),...,lambda(n)}is finite, then the operator (A) over tilde solving the eigenvalues problem, (A) over tilde psi(k)=lambda(k)psi(k), k=1,...,n, is uniquely defined by a given set of orthonormal vectors {psi(k)}(k=1)(n) satisfying the condition span {psi(k)}(k=1)(n) boolean AND dom (vertical bar A vertical bar(1/2))={0}. (C) 2007 Wiley-Vch Verlag GmbH & Co. KGaA, Weinheim.