Regular semigroups of endomorphisms of von Neumann factors (Q1810019)

The authors consider a class of semigroups, closed under cocycle perturbations, which they call regular, on a factor \({\mathfrak M}\) of arbitrary type, and show that for these semigroups the problem of regular extension has a ``generalized solution''. It is shown that a certain \(C_0\)-semigroup of endomorphisms of \(\beta(H)\) can be assigned to each regular semigroup \(\{\alpha_t\}_{t\geq 0}\), and this \(C_0\)-semigroup coincides with the regular extension of semigroups, whenever it exists.