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ON TENSOR PRODUCTS OF WEAK MIXING VECTOR SEQUENCES AND THEIR APPLICATIONS TO UNIQUELY E-WEAK MIXING C*-DYNAMICAL SYSTEMS

Part of: Markov processes Selfadjoint operator algebras Measure-theoretic ergodic theory

Published online by Cambridge University Press:  04 October 2011

FARRUKH MUKHAMEDOV
FARRUKH MUKHAMEDOV*
Affiliation:
Department of Computational and Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, P.O. Box, 141, 25710, Kuantan, Pahang, Malaysia (email: far75m@yandex.ru)
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Abstract

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We prove that, under certain conditions, uniform weak mixing (to zero) of the bounded sequences in Banach space implies uniform weak mixing of their tensor product. Moreover, we prove that ergodicity of tensor product of the sequences in Banach space implies their weak mixing. As applications of the results obtained, we prove that the tensor product of uniquely E-weak mixing C*-dynamical systems is also uniquely E-weak mixing.

Keywords

uniform weak mixingweak mixingergodicityuniquely E-weak mixingC*-dynamical system

MSC classification

Secondary: 46L35: Classifications of $C^*$-algebras 46L51: Noncommutative measure and integration 28D05: Measure-preserving transformations 60J99: None of the above, but in this section
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 85 , Issue 1 , February 2012 , pp. 46 - 59
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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