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Stability and Dichotomy of Positive Semigroups on $L_p$

Stephen J. Montgomery-Smith
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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 $σ(A)$.

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BibTeXRIS

Stephen J. Montgomery-Smith. 1999-12-06. Stability and Dichotomy of Positive Semigroups on $L_p$. https://arxiv.org/abs/math/9406211

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