**Stephen Montgomery-Smith, Stability and Dichotomy of Positive Semigroups on \(L_p\).**
*Proc. A.M.S. ***8**, (1996), 2433-2437.
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 \(\sigma(A)\).
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