Decomposition of operator semigroups on W*-algebras
  We consider semigroups of operators on a W$^*$-algebra and prove, under appropriate assumptions, the existence of a Jacobs-DeLeeuw-Glicksberg type decomposition. This decomposition splits the algebra into a "stable" and "reversible" part with respect to the semigroup and yields, among others, a structural approach to the Perron-Frobenius spectral theory for completely positive operators on W$^*$-algebras. 
Andr\'as B\'atkai, Ulrich Groh, D\'avid Kunszenti-Kov\'acs, Marco   Schreiber
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