ON TENSOR PRODUCTS OF WEAK MIXING VECTOR SEQUENCES AND THEIR APPLICATIONS TO UNIQUELY E-WEAK MIXING C*-DYNAMICAL SYSTEMS

Abstract

AbstractWe 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.