Characterization of mixed n-Jordan and pseudo n-Jordan homomorphisms


Masoumeh Neghabi, Abasalt Bodaghi, Abbas Zivari-Kazempour




In this article, a new notion of n-Jordan homomorphism namely the mixed n-Jordan homomorphism is introduced. It is proved that how a mixed (n + 1)-Jordan homomorphism can be a mixed n-Jordan homomorphism and vice versa. By means of some examples, it is shown that the mixed n-Jordan homo- morphisms are different from the n-Jordan homomorphisms and the pseudo n-Jordan homomorphisms. As a consequence, it shown that every mixed Jordan homomorphism from Banach algebraA into commutative semisimple Banach algebraB is automatically continuous. Under some mild conditions, every unital pseudo 3-Jordan homomorphism is a homomorphism.