Authors

1 Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran

2 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

Abstract

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-algebras is norm continuous.

Keywords

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[1] Bracic J., Moslehian M.S., On Aautomatic continuty of 3-homomorphisms on Banach algebra, Bull. Malays. Math. Sci., 30(2007), 195-200.
[2] Eshaghi Gordji M., n-Jodan Homomorphisms, Bull. Aust. Math. Soc., 80 (2009), 159-164.
[3] Eshaghi Gordgi M., Karimi T., and Kaboli Gharetapeh S., Approximately n-Jordan Homomorphisms on Banach Algebras, J. Ineq. Appl., (2009), 8.
[4] Hejazian S., Mirzavaziri M. and Moslehian M.S., n-Homomorphisms, Bull. Iranian Math. Soc., 1 (2005), 13-23.
[5] Honary T.G., Shayanpour H., Automatic Continuity of n-Homomorphisms Between Banach Algebras, Quaest. Math., 33 (2010), 189-196.
[6] Murphy G.J., C-algebras and Operator Theory, Acedemic Press, Sandiego, (1990).
[7] Park E., Trout J., On the nonexistence of nontrivial involutive n-homomorphisms of C-algebras, Trans. Amer. Math. Soc, 361(2009), 1949-1961.
[8] Tomforde M., Continiuty of ring -homomorphisms between C-algebras, New York J. Math. Soc., 15(2009), 161-167.
[9] Zelazko W., A characterization of multiplicative linear functionals in complex Banach algebras, Studia Math, 30(1968), 83-85.