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In this paper, we provide a sublinear function $p$ on ordered Banach spaces,which depends on the order structure of the space. With respect to this $p$, westudy the relation between $p$-contractivity of positive semigroups and the$p$-dissipativity of its generators. The positive off-diagonal property ofgenerators is also studied in ordered vector spaces.

Dissipativity and positive off-diagonal property of operators on ordered Banach spaces