Let X, Y be locally compact Hausdorff spaces and M, N be Banach algebras. Let θ: C0(X, M) → C0(Y, N) be a zero product preserving bounded linear map with dense range. We show that θ is given by a continuous field of algebra homomorphisms from M into N if N is irreducible. As corollaries, such a surjective θ arises from an algebra homomorphism, provided that M is a W*-algebra and N is a semi-simple Banach algebra, or both M and N are C*-algebras.
All Science Journal Classification (ASJC) codes