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Characterization of Pseudo n-Jordan Homomorphisms

  • Received : 2020.03.29
  • Accepted : 2021.07.06
  • Published : 2021.12.31

Abstract

In this paper, among other things, we show that under special hypotheses every [pseudo] (n + 1)-Jordan homomorphism is a [pseudo] n-Jordan homomorphism and vice versa.

Keywords

Acknowledgement

The author would like to thank the referees for proving valuable comments and helping in improving the content of this paper.

References

  1. G. An, Characterization of n-Jordan homomorphism, Linear Multi. Algebra, 66(4)(2018), 671-680. https://doi.org/10.1080/03081087.2017.1318818
  2. A. Bodaghi and H. Inceboz, n-Jordan homomorphisms on commutative algebras, Acta. Math. Univ. Comenianae., 87(1)(2018), 141-146.
  3. A. Bodaghi and H. Inceboz, Extension of Zelazko's theorem to n-Jordan homomorphisms, Adv. Pure. Appl. Math., 10(2)(2019), 165-170. https://doi.org/10.1515/apam-2016-0075
  4. A. Ebadian, A. Jabbari and N. Kanzi, n-Jordan homomorphisms and Pseudo n-Jordan homomorphisms on Banach algebras, Mediterr. J. Math., 14(241)(2017), 1-11. https://doi.org/10.1007/s00009-016-0833-2
  5. A. Ebadian, M. Eshaghi Gordji and A. Jabbari, Pseudo n-Jordan homomorphisms and pseudo n-homomorphisms on Banach algebras, Honam Math. J., 42(2)(2020), 411-423. https://doi.org/10.5831/HMJ.2020.42.2.411
  6. Sh. Hejazian, M. Mirzavaziri and M. S. Moslehian, n-homomorphisms, Bull. Iranian Math. Soc., 31(1)(2005), 13-23.
  7. I. N. Herstein, Jordan homomorphisms, Trans. Amer. Math. Soc., 81(1)(1956), 331-341. https://doi.org/10.1090/S0002-9947-1956-0076751-6
  8. N. Jacobson and C. E. Rickart, Jordan homomorphisms of rings, Trans. Amer. Math. Soc., 69(3)(1950), 479-502. https://doi.org/10.2307/1990495
  9. M. Neghabi, A. Bodaghi and A. Zivari Kazempour, Characterization of mixed n-Jordan homomorphisms and pseudo n-Jordan homomorphisms, Filomat, 34(6)(2020), 1989-2002. https://doi.org/10.2298/FIL2006989N
  10. T. Palmer, Banach algebras and the general theory of *-algebras. Vol I, Cambridge: Univ Press, (1994).
  11. W. Zelazko, A characterization of multiplicative linear functionals in complex Banach algebras, Studia Math., 30(1968), 83-85. https://doi.org/10.4064/sm-30-1-83-85
  12. A. Zivari-Kazempour, A characterization of 3-Jordan homomorphism on Banach algebras, Bull. Aust. Math. Soc., 93(2)(2016), 301-306. https://doi.org/10.1017/S0004972715001057
  13. A. Zivari-Kazempour, Automatic continuity of n-Jordan homomorphisms on Banach algebras, Commun. Korean Math. Soc., 33(1)(2018), 165-170. https://doi.org/10.4134/CKMS.c170071
  14. A. Zivari-Kazempour, Characterization of n-Jordan homomorphisms and automatic continuity of 3-Jordan homomorphisms on Banach algebras, Iran J. Sci. Technol. Trans. Sci., 44(2020), 213-218. https://doi.org/10.1007/s40995-019-00814-1