On tensor products of weak mixing vector sequences and their applications to uniquely E-weak mixing C*-dynamical systems
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 obtain...
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2012
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| Online Access: | http://irep.iium.edu.my/15976/1/mf-BulAusMathSoc%282012%29.pdf http://irep.iium.edu.my/15976/ http://dx.doi.org/10.1017/S0004972711002772 |
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| Summary: | 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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