Stability and dichotomy of positive semigroups on 𝐿_{𝑝}

Montgomery-Smith, Stephen

doi:10.1090/S0002-9939-96-03356-4

Stability and dichotomy of positive semigroups on $L_p$
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Proc. Amer. Math. Soc. 124 (1996), 2433-2437 Request permission

Abstract:

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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