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.

Mathematics Subject Classification (2010):

• 46H40
• 47A10

Key words:

• Almost Jordan homomorphism
• almost multiplicative maps
• Fréchet algebras
• Q-algebras
• automatic continuity