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 .
Positivity – Springer Journals
Published: Jan 1, 2014
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