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

摘要

We prove that, under certain conditions, uniform weak mixing (to zero) of thebounded sequences in Banach space implies uniform weak mixing of its tensorproduct. Moreover, we prove that ergodicity of tensor product of the sequencesin Banach space implies its weak mixing. Applications of the obtained results,we prove that tensor product of uniquely $E$-weak mixing $C^*$-dynamicalsystems is also uniquely $E$-weak mixing as well.