A Kadison transitivity theorem for C∗-semigroups

We prove a semigroup analogue of the Kadison Transitivity Theorem for C ∗ -algebras. Specifically, we show that a closed, homogeneous, self-adjoint, topologically transitive, semigroup of operators acting on a separable Hilbert space is (strictly) transitive if the semigroup contains a non-zero compact operator. Additional structural information about such semigroups is obtained, and examples are provided to demonstrate that the theorem is the best possible in the semigroup case.