Additive jointly separating maps and ring homomorphisms

Abstract

Let X and Y be compact Hausdorff spaces, E and F be real or complex normed spaces and be a subspace of . For a function , let be the cozero set of f. A pair of additive maps is said to be jointly separating if whenever . In this paper, first, we give a partial description of additive jointly separating maps between certain spaces of vector-valued continuous functions (including spaces of vector-valued Lipschitz functions, absolutely continuous functions and continuously differentiable functions). Then we apply the results to characterize continuous ring homomorphisms between certain Banach algebras of vector-valued continuous functions. In particular, the results provide some generalizations of the recent results on unital homomorphisms between vector-valued Lipschitz algebras, with a different approach.