On tensor products of weak mixing vector sequences and their applications to uniquely $E$-weak mixing $C^*$- dynamical systems

Authors

  • Farrukh Mukhamedov

Keywords:

Uniform weak mixing, weak mixing, ergodicity, uniquely E-weak mixing, $C^*$-dynamical system.

Abstract

We prove that, under certain conditions, uniform weak mixing (to zero) of the bounded sequences in Banach space implies uniform weak mixing of its tensor product. Moreover, we prove that ergodicity of tensor product of the sequences in Banach space implies its weak mixing. Applications of the obtained results, we prove that tensor product of uniquely $E$-weak mixing $C^*$-dynamical systems is also uniquely $E$-weak mixing as well. DOI: 10.1017/S0004972711002772

Published

2011-12-09

Issue

Vol. 85 No. 1 (2012)

Section

Articles
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