  Dilations of completely positive semigroups to endomorphism semigroups have
been studied by numerous authors. Most existing dilation theorems involve a
non-unital embedding, corresponding to the embedding of $B(H)$ as a corner of
$B(K)$ for Hilbert spaces $H \subset K$. A 1986 paper of Jean-Luc Sauvageot
shows how to achieve a unital dilation, but does not specify how to do so while
also preserving continuity properties of the original semigroup. This thesis
further develops Sauvageot's dilation theory in order to establish the
existence of continuous unital dilations, and to explore connections with free
probability.
