Frequently Hypercyclic Composition Operators on The Little Lipschitz Space of A Rooted Tree

Abstract We characterize the strictly increasing symbols $$\varphi :\mathbb {N}_0\longrightarrow \mathbb {N}_0$$ φ : N 0 ⟶ N 0 whose composition operators $$C_{\varphi }$$ C φ satisfy the Frequent Hypercyclicity Criterion on the little Lipschitz space $$\mathcal {L}_0(\mathbb {N}_0)$$ L 0 ( 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 $$\ell ^{\infty }$$ ℓ ∞ and $$c_0$$ 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.