$n$-Jordan homomorphisms on C-algebras

محورهای موضوعی : History and biography

A. Bodaghi ¹ (Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran)
B. Shojaee ² (Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran)

تاریخ دریافت : 1394/01/23 تاریخ پذیرش : 1394/01/23 تاریخ انتشار : 1390/12/11

کلید واژه: n-homomorphism, n-ring,

چکیده مقاله :

Let $n\in \mathbb{N}$. An additive map $h:A\to B$ between algebras $A$ and $B$ is called $n$-Jordan homomorphism if $h(a^n)=(h(a))^n$ for all $a\in A$. We show that every $n$-Jordan homomorphism between commutative Banach algebras is a $n$-ring homomorphism when $n < 8$.For these cases, every involutive $n$-Jordan homomorphism between commutative C-algebrasis norm continuous.

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