  We establish the relation between the Wigner-Weisskopf theory for the
description of an unstable system and the theory of coupling to an environment.
According to the Wigner-Weisskopf general approach, even within the pole
approximation (neglecting the background contribution) the evolution of a total
system subspace is not an exact semigroup for the multi-channel decay, unless
the projectors into eigesntates of the reduced evolution generator $W(z)$ are
orthogonal. In this case these projectors must be evaluated at different pole
locations $z_\alpha\neq z_\beta$. Since the orthogonality relation does not
generally hold at different values of $z$, for example, when there is symmetry
breaking, the semigroup evolution is a poor approximation for the multi-channel
decay, even for a very weak coupling. Nevertheless, there exists a possibility
not only to ensure the orthogonality of the $W(z)$ projectors regardless the
number of the poles, but also to simultaneously suppress the effect of the
background contribution. This possibility arises when the theory is generalized
to take into account interactions with an environment. In this case $W(z)$, and
hence its eigenvectors as well, are {\it independent} of $z$, which corresponds
to a structure of the coupling to the continuum spectrum associated with the
Markovian limit.
