Measurable bundles of \(C^*\) -dynamical systems and its applications

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• 作者：Inomjon Ganiev (1)
  Farrukh Mukhamedov (2)
  
• 关键词：Measurable bundle ; $$L_0$$ L 0 ; valued norms ; $$C^*$$ C 鈭?dynamical systems ; Ergodic ; Unique ergodicity ; 47A35 ; 17C65 ; 46L70 ; 46L52 ; 28D05
• 刊名：Positivity
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：18
• 期：4
• 页码：687-702
• 全文大小：252 KB
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• 作者单位：Inomjon Ganiev (1)
  Farrukh Mukhamedov (2)
  
  1. Department of Science in Engineering, International Islamic University Malaysia, P.O. Box 10, 50728聽, Kuala Lumpur, Malaysia
  2. Department of Computational and Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, P.O. Box 141, 25710聽, Kuantan, Pahang, Malaysia
  
• ISSN：1572-9281

文摘

In the present paper we investigate \(L_0\) -valued states and Markov operators on \( C^*\) -algebras over \(L_0\) . Here, \(L_0=L_0(\Omega )\) is the algebra of equivalence classes of complex measurable functions on \((\Omega ,\Sigma ,\mu )\) . In particular, we give representations for \(L_0\) -valued states and Markov operators on \(C^*\) -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 \( C^*\) -dynamical systems over \(L_0\) .