Stability and Dichotomy of Positive Semigroups on $L_p$

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 $\sigma (A)$.

References in corpus (1)

• Lyapunov theorems for Banach spaces