  A generalization of the Pistone-Sempi argument, demonstrating the utility of
non-commutative Orlicz spaces, is presented. The question of lifting positive
maps defined on von Neumann algebra to maps on corresponding noncommutative
Orlicz spaces is discussed. In particular, we describe those Jordan *-morphisms
on semifinite von Neumann algebras which in a canonical way induce quantum
composition operators on noncommutative Orlicz spaces. Consequently, it is
proved that the framework of noncommutative Orlicz spaces is well suited for an
analysis of large class of interesting noncommutative dynamical systems.
