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

Farrukh Mukhamedov

doi:10.1017/S0004972711002772

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

Farrukh Mukhamedov

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	46-59
Number of pages	14
Journal	Bulletin of the Australian Mathematical Society
Volume	85
Issue number	1
DOIs	https://doi.org/10.1017/S0004972711002772
Publication status	Published - Feb 2012
Externally published	Yes

Keywords

C*-dynamical system
ergodicity
uniform weak mixing
uniquely E-weak mixing
weak mixing

ASJC Scopus subject areas

Mathematics(all)

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10.1017/S0004972711002772

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AB - 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.

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KW - ergodicity

KW - uniform weak mixing

KW - uniquely E-weak mixing

KW - weak mixing

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

Abstract

Keywords

ASJC Scopus subject areas

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