A note on the hypercyclicity of operator-weighted shifts

Abstract

In this article, we give equivalent conditions for the hypercyclicity of bilateral operator-weighted shifts on $L^2\left(\mathcal{K}\right)$ with weight sequence $\{A_n{\}}_{n=-\infty }^{\infty }$ of positive invertible diagonal operators on a separable complex Hilbert space $\mathcal{K}$, as well as for hereditarily hypercyclicity and supercyclicity.