Abstract
Let δ be the generator of a strongly continuous one-parameter group of ∗-automorphisms of a C ∗ -algebra A . We prove that a densely defined operator K on A satisfying a certain second order locality condition with respect to δ must have the form K = Lδ + Mδ 2, where L and M are possibly unbounded central multipliers of the two-sided ideal generated by the range of δ. If K, in addition, is an invariant dissipation, then K is the generator of a strongly continuous one-parameter semigroup of completely positive contractions.
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