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Some results on $n$-Jordan homomorphisms
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With the motivation to extend the Zelasko's theorem on commutative algebras, it was shown in \cite{Eshaghi.2009} that if $n \in \{3, 4\}$ is fixed, $A, B$ are commutative algebras and $h:A\rightarrow B$ is an $n$-Jordan homomorphism, then $h$ is an $n$-ring homomorphism. In this paper, we extend this result for all $n\geq 3$.
Abstract
With the motivation to extend the Zelasko's theorem on commutative algebras, it was shown in \cite{Eshaghi.2009} that if $n \in \{3, 4\}$ is fixed, $A, B$ are commutative algebras and $h:A\rightarrow B$ is an $n$-Jordan homomorphism, then $h$ is an $n$-ring homomorphism. In this paper, we extend this result for all $n\geq 3$.
참고문헌 (6)
- J. Bracic, "On automatic continuity of 3-homomorphisms on Banach algebras", Bull. Malays. Math. Sci. Soc, 30(2), pp.195~200 (2007)
- M. ESHAGHI GORDJI, "n-Jordan homomorphisms", Bulletin of the Australian Mathematical Society, 80(1), pp.159~164 (2009), Cambridge University Press (CUP)[DOI]
- M. Eshaghi Gordji, "Approximately n-Jordan ho-momorphisms on Banach algebras", J. Inequal. Appl, 2009, pp.8~ (2019)[DOI]
- Takeshi Miura, "Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras", Journal of Inequalities and Applications, 2005(4), pp.735242~ (2005), Springer Science and Business Media LLC[DOI]
- Efton Park, "On the nonexistence of nontrivial involutive $n$-homomorphisms of $C^{\star }$-algebras", Transactions of the American Mathematical Society, 361(04), pp.1949~1961 (2009), American Mathematical Society (AMS)[DOI]
- W. Żelazko, "A characterization of multiplicative linear functionals in complex Banach algebras", Studia Mathematica, 30(1), pp.83~85 (1968), Institute of Mathematics, Polish Academy of Sciences[DOI]
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