| Abstract: | In the paper we obtain an ergodic decomposition generated by a positive operator T:E → E (E being a Banach lattice having the projection property). If T is a power bounded operator and if E is a KB-space, then the decomposition permits us to describe sufficient conditions for the existence of nonzero T-subinvariant elements in E. We also study the relationship between the Hopf decomposition in Banach lattices and the one defined in the paper in order to obtain sufficient conditions for the existence of a T-invariant weak order unit. |
