Disjoint hypercyclic weighted pseudoshift operators generated by different shifts

Abstract

Let $I$ be a countably infinite index set, and let $X$ be a Banach sequence space over $I$. In this article, we characterize the disjoint hypercyclic and supercyclic weighted pseudoshift operators on $X$ in terms of the weights, the OP-basis, and the shift mappings on $I$. Also, the shifts on weighted $L^p$ spaces of a directed tree and the operator weighted shifts on ${\ell }^2(\mathbb{Z},\mathcal{K})$ are investigated as special cases.