Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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PSEUDO n-JORDAN HOMOMORPHISMS AND PSEUDO n-HOMOMORPHISMS ON BANACH ALGEBRAS

  • Received : 2019.09.27
  • Accepted : 2020.04.02
  • Published : 2020.06.25
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Abstract

In this paper, we correct some errors and typos of [2] and introduce a new concept related to pseudo n-Jordan homomorphisms, that we call it pseudo n-homomorphism. We investigate automatic continuity and positivity of pseudo n-homomorphisms and pseudo n-Jordan homomorphisms on Banach algebras and C*-algebras. Moreover, we show that the sum of two pseudo n-Jordan homomorphisms is not a pseudo n-Jordan homomorphism and we show that under some conditions the sum of two pseudo n-Jordan homomorphisms is a pseudo n-Jordan homomorphism.

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Acknowledgement

The authors wish to thank the referees for the careful reading of the paper and for their useful comments.

References

  1. J. Bracic and M. S. Moslehian, On automatic continuity of 3-homomorphisms on Banach algebras, Bull. Malays. Math. Sci. Soc. 30(2)(2007), 195-200.
  2. A. Ebadian, A. Jabbari and N. Kanzi. n-Jordan homomorphisms and pseudo n-Jordan homomorphisms on Banach algebras, Mediterr. J. Math. 14(6) (2017),241. https://doi.org/10.1007/s00009-017-1041-4
  3. M. Eshaghi Gordji, A. Jabbari and E. Karapinar, Automatic continuity of surjective n-homomorphisms on Banach algebras, Bull. Iran. Math. Soc. 41(5) (2015), 1207-1211.
  4. Sh. Hejazian, M. Mirzavaziri and M. S. Moslehian, n-Homomorphisms, Bull. Iran. Math. Soc. 31(1) (2005), 13-23.
  5. T. G. Honari and H. Shayanpour, Automatic continuity of n-homomorphisms between Banach algebras, Q. Math. 33 (2010), 189-196. https://doi.org/10.2989/16073606.2010.491180
  6. T. G. Honari and H. Shayanpour, Automatic continuity of n-homomorphisms between topological algebras, Bull. Aust. Math. Soc. 83 (2011), 389-400. https://doi.org/10.1017/S0004972711002036
  7. M. E. Gordji, n-Jordan homomorphisms, Bull. Aust. Math. Soc. 80 (2009), 159-164. https://doi.org/10.1017/S000497270900032X
  8. M. Neghabi, A. Bodaghi and A. Zivari Kazempour, Characterization of mixed n-Jordan homomorphisms and pseudo n-Jordan homomorphisms, arXiv:1903.09577v1 [math.FA] 22 Mar 2019.
  9. E. Park and J. Trout, On the nonexistence of nontrivial involutive n-homomorphisms of C*-algebras, Trans. Amer. Math. Soc. 361 (2009), 19491961.