  We discuss unitarity constraints on the dynamics of a system of three
interacting particles. We show how the short-range interaction that describes
three-body resonances can be separated from the long-range exchange processes,
in particular the one-pion-exchange process. It is demonstrated that unitarity
demands a specific functional form of the amplitude with a clear
interpretation: the bare three-particle resonances are dressed by the initial-
and final-state interaction, in a way that is consistent with the considered
long-range forces. We postulate that the resonance kernel admits a
factorization in the energy variables of the initial- and the final-state
particles. The factorization assumption leads to an algebraic form for the
unitarity equations, which is reminiscent of the well-known two-body-unitarity
condition and approaches it in the limit of the narrow-resonance approximation.
