Non-Hermitian quantum-Hamiltonian-candidate combination H λ of a non-Hermitian unperturbed operator H = H 0 with an arbitrary “small” non-Hermitian perturbation λ W is given a mathematically consistent unitary-evolution amina muaddi scarpe trasparenti interpretation.The formalism generalizes the conventional constructive Rayleigh−Schrödinger perturbation expansion technique.It is sufficiently general to take into account the well known formal ambiguity of reconstruction of the correct physical Hilbert space of states.The possibility of removal of the ambiguity via bolia outlet gent a complete, irreducible set of observables is also discussed.