Recurrence for weighted pseudo-shift operators

In this work, we provide a characterization of multiply recurrent operators that act on a Fréchet space.As an application, we extend the weighted shift's results established by G. Costakis et al. in 9.We achieve this by characterizing topologically multiply recurrent pseudo-shifts acting on an F -sequence space indexed by an arbitrary countable infinite set.This characterization is in terms of the weights, the OP-basis and the shift mapping.Additionally, we establish that the recurrence and the hypercyclicity of pseudo-shifts are equivalent.