  The counterpart of the rotating wave approximation for non-Hermitian
Hamiltonians is considered, which allows for the derivation of a suitable
effective Hamiltonian for systems with some states undergoing decays. In the
limit of very high decay rates, on the basis of this effective description we
can predict the occurrence of a quantum Zeno dynamics which is interpreted as
the removal of some coupling terms and the vanishing of an operatorial
pseudo-Lamb shift.
