On unitary dilations of two-parameter semigroups of contractions and continuous commutant lifting

It is proved that every semigroup of contractions with parameter on Q(+) x Q(+) or Q(+) x N has a unitary dilation. The dilation result about Q(+) x Q(+) is used to obtain a new proof of the Slocinski dilation theorem, which says that every strongly continuous semigroup of contractions, with parameter on R+ x R+, has a strongly continuous unitary dilation. The result about Q(+) x N is used to obtain a new proof of the continuous version of the commutant lifting theorem.