Abstract. We consider positive perturbations of positive semigroups on AMspaces and prove a result which is the dual counterpart of a famous perturbation result of Desch in AL-spaces. As an application we present unbounded perturbations of the shift semigroup.

Abstract. We prove a Desch-Schappacher type perturbation theorem for strongly continuous and locally equicontinuous one-parameter semigroups which are defined on a sequentially complete locally convex space.

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We give a definition for positivity on an extrapolation space for positive strongly continuous semigroups. We prove a perturbation result on AM spaces for positive semigroups by positive operators. Finally, we give an example for this kind of perturbations. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)