Characterization of n-Jordan Homomorphisms and Automatic Continuity of 3-Jordan Homomorphisms on Banach Algebras

摘要

We show that every Banach algebra A is 3-Jordan functionally continuous. More especially, every 3-Jordan homomorphism from a Banach algebra A into a commutative semisimple Banach algebra B is automatically continuous. We also prove the same result for n-Jordan homomorphism (n > 4) with the additional hypothesis that the Banach algebra A is unital. A characterization of n-Jordan homomorphism for the special case n 2 {2; 3; 4} is also given.