Skip to main content

Characterization of n-Jordan Multipliers

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

Let A be a Banach algebra and X be a (Banach) A-bimodule. A linear map T : AX is called an n-Jordan multiplier if T(an) = aT(an− 1) for all aA. In this paper, among other things, we show that under special hypotheses every (n + 1)-Jordan multiplier is an n-Jordan multiplier and vice versa.

This is a preview of subscription content, access via your institution.

References

  1. Bodaghi, A., Inceboz, H.: n-Jordan homomorphisms on commutative algebras. Acta. Math. Univ. Comen. 87, 141–146 (2018)

    MathSciNet  MATH  Google Scholar 

  2. Fozouni, M.: n-Jordan multipliers. Surv. Math. Appl. 13, 121–129 (2018)

    MathSciNet  MATH  Google Scholar 

  3. Gahramani, H.: On centralizers of Banach algebras. Bull. Malay. Math. Sci. Soc. 38, 155–164 (2015)

    MathSciNet  Article  Google Scholar 

  4. Helgason, S.: Multipliers of Banach algebras. Ann. Math. 64, 240–254 (1956)

    MathSciNet  Article  Google Scholar 

  5. Johnson, B.E.: An introduction to the theory of centralizers. Proc. Lond. Math. Soc. 14, 299–320 (1964)

    MathSciNet  Article  Google Scholar 

  6. Laali, J., Fozouni, M.: n-multipliers and their relations with n-homomorphisms. Vietnam J. Math. 45, 451–457 (2017)

    MathSciNet  Article  Google Scholar 

  7. Larsen, R.: An Introduction to the Theory of Multipliers. Springer, Berlin (1971)

    Book  Google Scholar 

  8. Vukman, J.: An identity related to centralizers in semiprime rings. Comment. Math. Univ. Carolin. 40, 447–456 (1999)

    MathSciNet  MATH  Google Scholar 

  9. Wendel, J. G.: Left centralizers and isomorphisms of group algebras. Pac. J. Math. 2, 251–261 (1952)

    MathSciNet  Article  Google Scholar 

  10. Zalar, B.: On centralizers of semiprime rings. Comment. Math. Univ. Carolin. 32, 609–614 (1991)

    MathSciNet  MATH  Google Scholar 

  11. Zivari-Kazempour, A.: Almost multipliers of fréchet algebras. The J. Anal. 28, 1075–1084 (2020)

    MathSciNet  Article  Google Scholar 

Download references

Acknowledgements

The author gratefully acknowledges the helpful comments of the anonymous referees.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Abbas Zivari-Kazempour.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zivari-Kazempour, A. Characterization of n-Jordan Multipliers. Vietnam J. Math. 50, 87–94 (2022). https://doi.org/10.1007/s10013-021-00479-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10013-021-00479-7

Keywords

  • n-Multiplier
  • n-Jordan multiplier
  • Unitary Banach A-module

Mathematics Subject Classification (2010)

  • Primary 47B48
  • Secondary 46L05
  • 46H25