Department of Mathematics2024-11-1020070039-322310.4064/sm183-1-32-s2.0-38549118267http://dx.doi.org/10.4064/sm183-1-3https://hdl.handle.net/20.500.14288/17219Let A and B be semisimple commutative Banach algebras with bounded approximate identities. We investigate the problem of extending a homomorphism phi : A -> B to a homomorphism of the multiplier algebras M(A) and M(B) of A and B, respectively. Various sufficient conditions in terms of B (or B and phi) axe given that allow the construction of such extensions. We exhibit a number of classes of Banach algebras to which these criteria apply. In addition, we prove a polar decomposition for homomorphisms from A into A with closed range. Our results are applied to Fourier algebras of locally compact groups.MathematicsJournal Article1730-6337253217200003Q38781