  Quantum Markov Semigroups (QMSs) originally arose in the study of the
evolutions of irreversible open quantum systems. Mathematically, they are a
generalization of classical Markov semigroups where the underlying function
space is replaced by a non-commutative operator algebra. In the case when the
QMS is uniformly continuous, theorems due to Lindblad \cite{lindblad},
Stinespring \cite{stinespring}, and Kraus \cite{kraus} imply that the generator
of the semigroup has the form $$L(A)=\sum_{n=1}^{\infty}V_n^*AV_n +GA+AG^*$$
where $V_n$ and G are elements of the underlying operator algebra. In the
present paper we investigate the form of the generators of QMSs which are not
necessarily uniformly continuous and act on the bounded operators of a Hilbert
space. We prove that the generators of such semigroups have forms that reflect
the results of Lindblad and Stinespring. We also make some progress towards
forms reflecting Kraus' result. Lastly we look at several examples to clarify
our findings and verify that some of the unbounded operators we are using have
dense domains.
