Perturbation theory of PT-symmetric Hamiltonians
  In the framework of perturbation theory the reality of the perturbed eigenvalues of a class of $\PT$symmetric Hamiltonians is proved using stability techniques. We apply this method to $\PT$symmetric unperturbed Hamiltonians perturbed by $\PT$symmetric additional interactions. 
E. Caliceti, F. Cannata, S. Graffi