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

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

2010-09-03

arxiv.org/abs/1009.0583v3

Bull, Aus. Math. Soc. 85(2012), 46-59

Mathematics

Functional Analysis

14 pages

Scientific paper

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.

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