Frequently hypercyclic composition operators on the little Lipschitz space of a rooted tree

We characterize the strictly increasing symbols $\phi :{\mathbb{N}}_0⟶{\mathbb{N}}_0$ whose composition operators $C_{\phi }$ satisfy the Frequent Hypercyclicity Criterion on the little Lipschitz space ${\mathcal{L}}_0({\mathbb{N}}_0)$. With this result we continue the recent research about this kind of spaces and operators, but our approach relies on establishing a natural isomorphism between the Lipschitz-type spaces over rooted trees and the classical spaces ${\mathrm{\ell }}^{\mathrm{\infty }}$ and $c_0$. Such isomorphism provides an alternative framework that simplifies and allows to improve many previous results about these spaces and the operators defined there.