Abstract
Let A and B be generators of analytic semigroups in a Banach space. Under some conditions on the commutator of the resolvents of A and B, already considered in the literature and not implying relative boundedness, we prove that the closure of A+B (or a proper extension of it) also generates an analytic semigroup, and we characterize interpolation spaces related to it. As a tool, we use approximation and interpolation results for multivalued linear operators.
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