n-Jordan homomorphisms on commutative algebras
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Abstract
It is proved that every n-Jordan homomorphism between commutative algebras is an n-ring homomorphism when n is an arbitrary and xed positive integer number. We employ this result to show that every involutive n-Jordan homomorphism between commutative C*-algebras is automatically norm continuous.
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How to Cite
Bodaghi, A., & Inceboz, H.
(2018).
n-Jordan homomorphisms on commutative algebras.
Acta Mathematica Universitatis Comenianae, 87(1), 141-146.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/635/569
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References
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[2] A. Bodaghi, n-homomorphism amenability, Proc. Rom. Aca., Series A, 14, No.2 (2013), 101-105.
[3] A. Bodaghi and B. Shojaee, n-Jordan homomorphisms on C*-algebras, J. Lin. Topo. Alg., 1, No.1 (2012), 1-7.
[4] J. Bracic and M. S. Moslehian. On automatic continuity of 3-homomorphisms on Banach algebra, Bull. Malays. Math. Sci. 30(2) (2007), 195-200.
[5] M. Bresar, W. S. Martindale and C. R. Miers, Maps preserving nth powers, Comm. Algebra, 26 (1998), no. 1, 117-138.
[6] M. Eshaghi Gordji. n-Jodan Homomorphisms, Bull. Aust. Math. Soc. 80 (2009), 159-164.
[7] E. Gselmann, On approximate n-Jordan homomorphisms, Annales Mathematicae Silesianae. 28 (2014), 47-58.
[8] S. Hejazian, M. Mirzavaziri, and M. S. Moslehian, n-Homomorphisms, Bull. Iranian Math. Soc. 31, no. 1 (2005), 13-23.
[9] I. N. Herstein,Jordan homomorphisms, Trans. Amer. Math. Soc. 81 (1956), 331-341.
[10] T. G. Honary, H. Shayanpour. Automatic continuity of n-homomorphisms between Banach algebras, Quaest. Math., 33 (2010), 189-196.
[11] N. Jacobson and C. E. Rickart, Jordan homomorphisms of rings, Trans. Amer. Math. Soc. 69, (1950), 479-502.
[12] I. Kaplansky, Semi-automorphisms of rings, Duke Math. J. 14 (1947), 521-525.
[13] Y. H. Lee, Stability of n-Jordan homomorphisms from a normed algebra to a Banach algebra, Abst. Appli. Anal. 2013, Article ID 691025, 5 pages.
[14] E. Park and J. Trout, On the nonexistence of nontrivial involutive n-homomorphisms of C*-algebras, Trans. Amer. Math. Soc, 361 (2009), 1949-1961.
[15] W. Zelazko, A characterization of multiplicative linear functionals in complex Banach algebras, Studia Math, 30 (1968), 83-85.