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In this paper, we consider positive Desch-Schappacher perturbations ofbi-continuous semigroups on $\mathrm{AM}$-spaces with an additional propertyconcerning the additional locally convex topology. As an examples, we discussperturbations of the left-translation semigroup on the space of boundedcontinuous function on the real line and on the space of bounded linearoperators.

Positive Desch-Schappacher perturbations of bi-continuous semigroups on $\mathrm{AM}$-spaces