Weighted composition operators on the predual and dual Banach spaces of Beurling algebras on Z

Let v be a weight sequence on Z and let ψ,φ be complex-valued functions on Z such that φ(Z)⊂Z. In this paper we study the boundedness, compactness and weak compactness of weighted composition operators Cψ,φ on predual Banach spaces c0(Z,1/v) and dual Banach spaces ℓ∞(Z,1/v) of Beurling algebras ℓ1(Z,v).