مشخصه‌سازي n– همريختي‌هاي جردن روي جبرها

Characterization of n–Jordan homomorphisms on Banach algebras

در اين مقاله، نشان مي دهيم كه هر n-همريختي جردن φ از يك جبر يكدار A به يك جبر φ-جابجايي B كه در شرط زير صدق مي كند يك n-همريختي است. (φ(a^2 )=0⟹φ(a)=0 (a∈A ).

In this paper we prove that every n-Jordan homomorphis varphi:mathcal {A} longrightarrowmathcal {B} from unital Banach algebras mathcal {A} into varphi -commutative Banach algebra mathcal {B} satisfiying the condition varphi (x^2)=0 Longrightarrow varphi (x)=0، xin mathcal {A}، is an n-homomorphism. In this paper we prove that every n-Jordan homomorphism varphi:mathcal {A} longrightarrowmathcal {B} from unital Banach algebras $mathcal{A} into varphi$-commutative Banach algebra $mathcal {B}. satisfiying the condition varphi (x^2)=0 Longrightarrow varphi (x)=0، xin mathcal {A}، is an n-homomorphism. This result was proved in cite {zivari1} for 3-Jordan homomorphism with the additional hypothesis that the Banach algebra mathcal {A} is unital، and it is extended for all nin mathbb {N} in cite {An}. Later، for nin lbrace 3،4 rbrace، Theorem ref {T1} proved in cite {Bodaghi1} by considering an extra condition varphi (ab^2)= varphi (b^2a)، (a،bin mathcal {A}). Some significant results concerning Jordan homomorphisms and their automatic continuity on Banach algebras obtained by the author in cite {zivari}، cite {zivari2} and cite {zivari3}. In this paper، under special hypotheses we prove that every n-Jordan homomorphism varphi from Banach algebra mathcal {A} into Banach algebra mathcal {B} is an n-homomorphism.