الملخص

In this paper, we generalized the Jewell-Sinclair theorem to include not only associative Banach algebra but also the nonassociative Banach algebra. Our methods in extend Jewell-Sinclair theorem is based on the theory of multiplication algebra of an arbitrary algebra and another techniques, which is the standard method in the nonassociative context in the Spanish school. Furthermore, we give as an application example of our generalization for the Jewell-Sinclair theorem the well-known result proved by Rodriguez that assert the automatic continuity of a surjective homomorphisim on a nonassociative f f*- algebras, Our proof is based on essence the same lines of Rodriguez proof.