The character space of vector-valued Lipschitz algebras

Abstract

Let B be a subalgebra of a commutative Banach algebra A. In this paper, we investigate conditions for that A and B have the same character space. Moreover, we determine the character space of the vector-valued Lipschitz algebra Lip_{d}(X,E), where (X,d) is any metric space and $E$ is a certain unital semisimple commutative *-Banach algebra.