Determinacy of Bounded Complex Perturbations of Jacobi Matrices

We consider complex Jacobi matrices G which can be decomposed in the form G=J+C, where J is a real Jacobi matrix and C is a complex Jacobi matrix whose entries are uniformly bounded. We prove that the determinacy of the operator defined by G is equivalent to that of J. From this we deduce that the determinacy of G is equivalent to the coincidence between the domains of definition of the operators G and its adjoint G*.