Compact homomorphisms between algebras of \(C(K)\)-valued Lipschitz functions (Q1659300)

The paper under review contains an improvement of a result of \textit{S.-H. Oi} [J. Math. Anal. Appl. 444, No. 1, 210--229 (2016; Zbl 1366.46038)]. More specifically, the authors provide a complete description of homomorphisms between two Banach algebras of Lipschitz functions with values in the continuous functions. Moreover, inspired by \textit{H. Kamowitz} and \textit{S. Scheinberg} [Stud. Math. 96, No. 3, 255--261 (1990; Zbl 0713.47030)], they also characterize the compactness of those homomorphisms.