Dynamics of weighted shifts on ℓp-sums and c0-sums

Official URL: https://dx.doi.org/10.1016/j.aim.2025.110250

We investigate a generalization of weighted shifts where each weight wk is replaced by an operator Tk going from a Banach space Xk to another one Xk−1. We then look if the obtained shift operator B(Tk) defined on the ℓp-sum (or the c0-sum) of the spaces Xk is hypercyclic, weakly mixing, mixing, chaotic or frequently hypercyclic. We also compare the dynamical properties of T and of the corresponding shift operator BT. Finally, we interpret some classical criteria in Linear Dynamics in terms of the dynamical properties of a shift operator.