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 \(\sigma(A)\). (tex, dvi, ps, pdf.)


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