Sums and commutators of generators of noncommuting strongly continuous groups

We consider two infinitesimal generators A, B of strongly continuous groups in a general Banach space X, such that either the commutator between A and B commutes both with etA and with etB, or the commutator is a multiple of A. We prove that under suitable assumptions the sum A + B and the commutator [A,B] are closable, and their closures generate strongly continuous groups. We give explicit representation formulas for such groups, in terms of etA and etB.  2002 Elsevier Science (USA). All rights reserved.