Automatic continuity of dense range n-homomorphisms

In this paper, we investigate the automatic continuity of n-homomorphisms and n-Jordan homomorphisms between Banach algebras, and generalize some well-known results concerning the automatic continuity of homomorphisms and Jordan homomorphisms. In particular, we generalize a Rickart's theorem for dense range n-homomorphisms with the additional hypothesis that the Banach algebra A is unital.