Disjoint Hypercyclic Powers of Weighted Pseudo-Shifts

Abstract

In this paper, we characterize disjoint hypercyclic powers of weighted pseudo-shifts on an arbitrary F-sequence space. As a special case, we deduce the equivalent conditions for the disjoint hypercyclicity of finitely many different powers of weighted shifts on \(\ell ^2({\mathbb {Z},\mathcal {K}})\) with weight sequence \(\{A_n\}_{n=-\infty }^{\infty }\) of positive invertible diagonal operators on \(\mathcal {K}\).