Published online by Cambridge University Press: 13 October 2009
The eigenvectors of an ergodic semigroup of linear normal positive unital maps on a von Neumann algebra are described. Moreover, it is shown by means of examples that mere positivity of the maps in question is not sufficient for Frobenius theory as in Albeverio and Høegh-Krohn [Frobenius theory of positive maps of von Neumann algebras. Comm. Math. Phys.64 (1978), 83–94] to hold.