# Measurable bundles of $$C^*$$ C ∗ -dynamical systems and its applications

Measurable bundles of $$C^*$$ C ∗ -dynamical systems and its applications In the present paper we investigate $$L_0$$ L 0 -valued states and Markov operators on $$C^*$$ C ∗ -algebras over $$L_0$$ L 0 . Here, $$L_0=L_0(\Omega )$$ L 0 = L 0 ( Ω ) is the algebra of equivalence classes of complex measurable functions on $$(\Omega ,\Sigma ,\mu )$$ ( Ω , Σ , μ ) . In particular, we give representations for $$L_0$$ L 0 -valued states and Markov operators on $$C^*$$ C ∗ -algebras over $$L_0$$ L 0 , respectively, as measurable bundles of states and Markov operators. Moreover, we apply the obtained representations to study certain ergodic properties of $$C^*$$ C ∗ -dynamical systems over $$L_0$$ L 0 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Measurable bundles of $$C^*$$ C ∗ -dynamical systems and its applications

16 pages

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### Abstract

In the present paper we investigate $$L_0$$ L 0 -valued states and Markov operators on $$C^*$$ C ∗ -algebras over $$L_0$$ L 0 . Here, $$L_0=L_0(\Omega )$$ L 0 = L 0 ( Ω ) is the algebra of equivalence classes of complex measurable functions on $$(\Omega ,\Sigma ,\mu )$$ ( Ω , Σ , μ ) . In particular, we give representations for $$L_0$$ L 0 -valued states and Markov operators on $$C^*$$ C ∗ -algebras over $$L_0$$ L 0 , respectively, as measurable bundles of states and Markov operators. Moreover, we apply the obtained representations to study certain ergodic properties of $$C^*$$ C ∗ -dynamical systems over $$L_0$$ L 0 .

### Journal

PositivitySpringer Journals

Published: Jan 1, 2014

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