  A theorem of Hegerfeldt shows that if the spectrum of the Hamiltonian is
bounded from below, then the propagation speed of certain probabilities does
not have an upper bound. We prove a theorem analogous to Hegerfeldt's that
appertains to asymmetric time evolutions given by a semigroup of operators. As
an application, we consider a characterization of relativistic quasistable
states by irreducible representations of the causal Poincare semigroup and
study the implications of the new theorem for this special case.
