  In the developing theory of infinite-dimensional quantum channels the
relevance of the energy-constrained diamond norms was recently corroborated
both from physical and information-theoretic points of view. In this paper we
study necessary and sufficient conditions for differentiability with respect to
these norms of the strongly continuous semigroups of quantum channels (quantum
dynamical semigroups). We show that these conditions can be expressed in terms
of the generator of the semigroup. We also analyze conditions for
representation of a strongly continuous semigroup of quantum channels as an
exponential series converging w.r.t. the energy-constrained diamond norm.
Examples of semigroups having such a representation are presented.
