Automatic Continuity of N-Homomorphisms between Banach Algebras

Abstract

An n-homomorphism between algebras is a linear map θ: A→B such that θ(a ₁ a ₂…a_n ) = θ(a₁)θ(a₂)…θ(a_n ) for all elements a ₁,a ₂…, an ∈ A. If A is a unital algebra it is known that every n-homomorphism is a multiple of a homomorphism. In this paper we extend some results of automatic continuity for n-homomorphisms between Banach algebras. The main results are the extensions of Johnson's theorem as well as a theorem due to C.E. Rickart for n-homomorphisms.