Geodesic
Majorization of $C_0$-semigroups in ordered Banach spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 1, pp. 47-54.

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We give criteria for domination of strongly continuous semigroups in ordered Banach spaces that are not necessarily lattices, and thus obtain generalizations of certain results known in the lattice case. We give applications to semigroups generated by differential operators in function spaces which are not lattices.
Classification : 34C11, 34C12, 34G10, 47B60, 47D06
Keywords: domination of semigroups; ordered Banach spaces; quasimonotonicity 
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Herzog, Gerd; Kunstmann, Peer Christian. Majorization of $C_0$-semigroups in ordered Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 1, pp. 47-54. http://geodesic.mathdoc.fr/item/CMUC_2006__47_1_a4/