  In the Feshbach projection operator formalism, resonance as well as decay
phenomena are described by means of the complex eigenvalues and eigenfunctions
of the non-Hermitian Hamilton operator $H_{\rm eff}$ that appears in an
intermediate stage of the formalism. The formalism can be applied for the
description of isolated resonances as well as for resonances in the overlapping
regime. Time asymmetry is related to the time operator which is a part of
$H_{\rm eff}$. An expression for the decay rates of resonance states is
derived. For isolated resonance states $\lambda$, this expression gives the
fundamental relation $\tau_\lambda = \hbar / \Gamma_\lambda$ between life time
and width of a resonance state. A similar relation holds for the average values
obtained for narrow resonances superposed by a smooth background term. In the
cross over between these two cases (regime of overlapping resonances), the
decay rate decreases monotonously as a function of increasing time.
