Domains of infinitesimal generators of automorphism flows

We present a systematic characterization of the domain of a generator of a one parameter group on certain C∗-subalgebras of L(H) via finite-dimensional estimates. Our approach yields an example of a densely defined closed symmetric derivation on a C∗-subalgebras of L(H) whose domain is not closed with respect to the C1-functional calculus. This completes and complements the earlier example of McIntosh (J. Funct. Anal. 30 (1977) 264). Our methods are partly based on the theory of adjoint C0-semigroups.