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We consider positive operator semigroups on ordered Banach spaces and study the relation of their long time behaviour to two different domination properties. First, we analyse under which conditions almost periodicity and mean ergodicity of a semigroup $$\mathcal {T}$$ T are inherited by other semigroups which are asymptotically dominated by $$\mathcal {T}$$ T . Then, we consider semigroups...
Generalizing a result of Keicher [4] we show that generators of positive C0-semigroups on super-atomic Banach lattices have trivial peripheral point spectrum provided they satisfy a certain growth condition.
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