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ON THE CHARACTER SPACE OF VECTOR-VALUED LIPSCHITZ ALGEBRAS

We show that the character space of the vector-valued Lipschitz algebra Lip � (X;E) of order , is homeomorphic to the cartesian product X ME in the product topology, where X is a compact metric space and E is a unital commutative Banach alge- bra. We also characterize the form of each character on Lip � (X;E). By appealing to the injective tensor product, we then identify the character space of the vector-valued polynomial Lipschitz al- gebra Lip � (X;E), generated by the polynomials on the compact space X C n . It is also shown that Lip � (X;E) is the injective tensor product Lip � (X)b ϵE. Finally, we characterize the form of each character on Lip � (X;E).