S. Montgomerysmith, STABILITY AND DICHOTOMY OF POSITIVE SEMIGROUPS ON L(P), Proceedings of the American Mathematical Society, 124(8), 1996, pp. 2433-2437
A new proof of a result of Lutz Weis is given, that states that the st
ability of a positive strongly continuous semigroup (e(tA))(t greater
than or equal to 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).