On the equivalence of some projection operator techniques

It is shown that equations of motion for mean values of operators derived from the time-convolution (time-convolutionless) generalized master equation for the density matrix and from the equations for operators from the Mori (Tokuyama-Mori) theory are the same, provided that projectors are suitably chosen. This is valid also for systems described by time-dependent Hamiltonians. We can emphasize that the equivalence of the correponding equations remains valid when invoking approximations.