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

TL;DR

This paper characterizes homomorphisms between Banach algebras of Lipschitz functions valued in continuous functions, providing a complete description and criteria for their compactness.

Contribution

It offers a comprehensive characterization of homomorphisms and their compactness in algebras of $C(K)$-valued Lipschitz functions, advancing understanding in functional analysis.

Findings

Complete description of homomorphisms between these algebras

Characterization of when such homomorphisms are compact

New criteria for compactness in this context

Abstract

We give a complete description of homomorphisms between two Banach algebras of Lipschitz functions with values in continuous functions. We also characterize the compactness of those homomorphisms.