Stability and Dichotomy of Positive Semigroups on $L_p$

Details Stability and Dichotomy of Positive Semigroups on $L_p$ Stability and Dichotomy of Positive Semigroups on $L_p$

1994-06-07

arxiv.org/abs/math/9406211v2

Proc. A.M.S. 8, (1996), 2433-2437

Mathematics

Functional Analysis

Scientific paper

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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