  In this paper we introduce a new decomposition of power-bounded operators,
analogous to the Jacobs-deLeeuw-Glicksberg decomposition. This is done using
so-called K\"ohler semigroups and the general theory of right topological
compact semigroups. This leads to a new proof, under appropriate assumptions,
of the cyclicity of the peripheral spectrum of positive operators on Banach
lattices.

Functional Analysis;Representation Theory