  A new proof of a result of Lutz Weis is given, that states that the stability
of a positive strongly continuous semigroup $(e^{tA})_{t \ge 0}$ on $L_p$ may
be determined by the quantity $s(A)$. We also give an example to show that the
dichotomy of the semigroup may not always be determined by the spectrum
$\sigma(A)$.
