Almost Jordan homomorphisms on Fréchet algebras

Abstract

In this paper we study the notation of almost Jordan homomorphism between Fréchet algebras. We show that if (A, (p _n )) is a Fréchet algebra and T : A → ℂ is a almost Jordan homomorphism, then either T is homomorphism, or it is continuous. Moreover, we prove that every almost Jordan homomorphism between two commutative Fréchet algebras A and B is a almost homomorphism. We also investigate automatic continuity of almost Jordan homomorphism between Fréchet Q-algebras.