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

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 $C^{\ast }$-dynamical systems is also uniquely $E$-weak mixing as well.

14 pages

References in corpus (4)

• Unique ergodicity of free shifts and some other automorphisms of C*-algebras
• Strict weak mixing of some C*-dynamical systems based on free shifts
• Joinings of W*-dynamical systems
• Ergodic properties of Bogoliubov automorphisms in free probability