On approximate n-Jordan homomorphisms

Eszter Gselmann

Published: 2014-09-30

Vol. 28 (2014)

On approximate n-Jordan homomorphisms

Eszter Gselmann

Abstract

The aim of this paper it to characterize n-Jordan homomorphisms and to investigate their connection with n-homomorphisms as well as homomorphisms. Furthermore, the following implication is also verified: if a function ϕ is additive and (for a fixed integer n≥2) the mapping x ↦ ϕ(xⁿ)-ϕ(x)ⁿ satisfies some mild regularity assumption, then the function ϕ is an n-homomorphism or it is a continuous additive function.

Keywords:

homomorphism , Jordan homomorphism , n-(Jordan) homomorphism , polynomial function

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Gselmann, E. (2014). On approximate n-Jordan homomorphisms. Annales Mathematicae Silesianae, 28, 47–58. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13990

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References

1. Ancochea G., Le théorème de von Staudt en géométrie projective quaternionienne, J. Reine Angew. Math. 184 (1942), 193–198.
2. Badora R., On approximate ring homomorphisms, J. Math. Anal. Appl. 276 (2002), no. 2, 589–597.
3. Brešar M., Martindale 3rd W.S., Miers C.R., Maps preserving n-th powers, Comm. Algebra 26 (1998), no. 1, 117–138.
4. Eshaghi Gordji M., n-Jordan homomorphisms, Bull. Aust. Math. Soc. 80 (2009), no. 1, 159–164.
5. Hejazian Sh., Mirzavaziri M., Moslehian M.S., n-homomorphisms, Bull. Iranian Math. Soc. 31 (2005), no. 1, 13–23.
6. Herstein I.N., Jordan homomorphisms, Trans. Amer. Math. Soc. 81 (1956), 331–341.
7. Jacobson N., Rickart C.E., Jordan homomorphisms of rings, Trans. Amer. Math. Soc. 69 (1950), 479–502.
8. Kaplansky I., Semi-automorphisms of rings, Duke Math. J. 14 (1947), 521–525.
9. Kuczma M., An introduction to the theory of functional equations and inequalities. Cauchy’s equation and Jensen’s inequality, Second edition, Birkhäuser Verlag, Basel, 2009.
10. Šemrl M., Nonlinear perturbations of homomorphisms on C(X), Quart. J. Math. Oxford Ser. (2) 50 (1999), no. 197, 87–109.
11. Šemrl P., Almost multiplicative functions and almost linear multiplicative functionals, Aequationes Math. 63 (2002), no. 1–2, 180–192.
12. Székelyhidi L., Regularity properties of polynomials on groups, Acta Math. Hungar. 45 (1985), no. 1–2, 15–19.
13. Żelazko W., A characterization of multiplicative linear functionals in complex Banach algebras, Studia Math. 30 (1968), 83–85. Google Scholar

Vol. 28 (2014)
Published: 2014-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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