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The eigenvectors of an ergodic semigroup of linear normal positive unitalmaps on a von Neumann algebra are described. Moreover, it is shown by means ofexamples, that mere positivity of the maps in question is not sufficient forFrobenius theory as in S. Albeverio and R. H\{o}egh-Krohn, \emph{Frobeniustheory of positive maps of von Neumann algebras}, Comm. Math. Phys. \textbf{64}(1978), 83--94, to hold.

The eigenvectors of semigroups of positive maps on von Neumann algebras