Abstract
One obtains a general theorem concerning the multiplicative perturbation of the generator of a strongly continuous semigroup on a Banach space, by a linear operator (bounded, but not necessarily with bounded inverse). This is used to derive a result, intimately related to time change in Markov processes, which extends a theorem of Dorroh (and gives an affirmative answer for the only situation which still remained in doubt in the context of Dorroh’s theorem). As an example of other possible applications, the general theorem is then used to obtain a result on the perturbation of the laplacian in L 2 (R n ).
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