Measurable bundles of $C^{\ast }$-dynamical systems and its applications

Abstract

In the present paper we investigate $L_0$-valued states and Markov operators on $C^{\ast }$-algebras over $L_0$. In particular, we give representations for $L_0$-valued state and Markov operators on $C^{\ast }$ algebras over $L_0$, respectively, as measurable bundles of states and Markov operators. Moreover, we apply the obtained representations to study certain ergodic properties of $C^{\ast }$-dynamical systems over $L_0$.