Recurrence of Composition Operators on Discrete Banach Spaces

Let (T,d) be an unbounded and locally finite metric space that contains a distinguished element o. Let L∞(T) denote the discrete Banach space and L0(T) its subspace of functions vanishing at infinity. First, we establish that the recurrence of a composition operator on the L0(T) space is equivalent to its rigidity. We then provide an equivalent characterization for the uniformly rigid and F-recurrence of Cφ. For the L∞(T) space, the recurrence of the operator is equivalent to the periodicity of the function φ. Second, we explore the concept of disjoint topological recurrence associated with multiple composition operators.