On dilation theory for c(0)-semigroups on Hilbert space

Given a commuting family (T-1,...,T-N) of bounded co-semigroups on Hilbert space, we establish a necessary and sufficient condition under which (T-1,...,T-N) admits a unitary dilation up to similarity. We apply it to show that this holds provided that each T-j is a contraction semigroup and, when N greater than or equal to 3, the semigroups T-1,...,TN-2 are analytic.