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We characterize the domain in L p -space of generators of submarkovian semigroups in terms of the form domain in L 2 and give the corresponding inequality. Using this inequality we obtain a criterion for the formal difference A-B of such generators to be a generator of a contraction semigroup in L p . The conditions on perturbation are expressed in terms of forms, i.e., in L 2 - terms

Some inequalities for sub-Markovian generators and their applications to the perturbation theory