We define a property of strong-mixing in the theory of $C^*$-dynamical systems and show that the property follows from the existence of a base of Walsh type. Moreover as applications we analyze covariant representations of chaotic dynamical systems.
"Covariant Representations Associated with Chaotic Dynamical Systems." Tokyo J. Math. 20 (1) 205 - 217, June 1997. https://doi.org/10.3836/tjm/1270042409