Decomposition of operator semigroups on W*-algebras

Abstract

We consider semigroups of operators on a W${}^{\ast }$-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${}^{\ast }$-algebras.

arXiv commentreferee's comments incorporated. To appear in Semigroup Forum

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