Skip to main content
SpringerLink
Log in

Reflexive–EP Elements in Rings

  • Published:
Bulletin of the Malaysian Mathematical Sciences Society Aims and scope Submit manuscript

Abstract

We define and characterize reflexive–EP elements in rings, that is elements which commute with their image-kernel (p, q)-inverse.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Baksalary, O.M., Trenkler, G.: Characterizations of EP, normal and Hermitian matrices. Linear Multilinear Algebra 56, 299–304 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ben-Israel, A., Greville, T.N.E.: Generalized Inverses: Theory and Applications, 2nd edn. Springer, New York (2003)

    MATH  Google Scholar 

  3. Boasso, E.: On the Moore–Penrose inverse, EP Banach space operators, and EP Banach algebra elements. J. Math. Anal. Appl. 339, 1003–1014 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Boasso, E.: Factorizations of EP Banach space operators and EP Banach algebra elements. J. Math. Anal. Appl. 379, 245–255 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Boasso, E., Djordjević, D.S., Mosić, D.: Weighted Moore–Penrose invertible and weighted EP Banach algebra elements. J. Korean Math. Soc. 50(6), 1349–1367 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cao, J., Xue, Y.: The characterizations and representations for the generalized inverses with prescribed idempotents in Banach algebras. FILOMAT 27(5), 851–863 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  7. Djordjević, D.S., Koliha, J.J.: Characterizing Hermitian, normal and EP operators. Filomat 21(1), 39–54 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Djordjević, D.S., Koliha, J.J., Straškraba, I.: Factorization of EP elements in \(C^*\)-algebras. Linear Multilinear Algebra 57(6), 587–594 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Djordjevic, D.S., Wei, Y.: Outer generalized inverses in rings. Commun. Algebra 33, 3051–3060 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. Drivaliaris, D., Karanasios, S., Pappas, D.: Factorizations of EP operators. Liner Algebra Appl. 429(7), 1555–1567 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Harte, R., Mbekhta, M.: On generalized inverses in \(C^*\)-algebras. Studia Math. 103, 71–77 (1992)

    MathSciNet  MATH  Google Scholar 

  12. Kantún-Montiel, G.: Outer generalized inverses with prescribed ideals. Linear Multilinear Algebra. 62(9), 1187–1196 (2014)

  13. Koliha, J.J.: A generalized Drazin inverse. Glasg. Math. J. 38, 367–381 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  14. Kolundžija, M.Z., Mosić, D., Djordjević, D.S.: Further results on the generalized Drazin inverse of block matrices in Banach algebras. Bull. Malays. Math. Sci. Soc. 38(2), 483–498 (2015)

  15. Liao, Y., Chen, J., Cui, J.: Cline’s formula for the generalized Drazin inverse. Bull. Malays. Math. Sci. Soc. (2) 37(1), 37–42 (2014)

    MathSciNet  MATH  Google Scholar 

  16. Mosić, D.: Some representations for the generalized Drazin inverse of block matrices in Banach algebras. Bull. Malays. Math. Sci. Soc. 37(4), 1137–1147 (2014)

  17. Mosić, D., Djordjević, D.S.: Partial isometries and EP elements in rings with involution. Electron. J. Linear Algebra 18, 761–772 (2009)

    MathSciNet  MATH  Google Scholar 

  18. Mosić, D., Djordjević, D.S.: Weighted–EP elements in \(C^*\)-algebras. Electron. J. Linear Algebra 22, 912–930 (2011)

    MathSciNet  MATH  Google Scholar 

  19. Mosić, D., Djordjević, D.S.: Factorization of weighted–EP elements in \(C^*\)-algebras. Appl. Math. Comput. 218(9), 5383–5390 (2012)

    MathSciNet  MATH  Google Scholar 

  20. Mosić, D., Djordjević, D.S., Koliha, J.J.: EP elements in rings. Linear Algebra Appl. 431, 527–535 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  21. Tian, Y., Wang, H.: Characterizations of EP matrices and weighted–EP matrices. Linear Algebra Appl. 434(5), 1295–1318 (2011)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The author is very grateful to the referees for constructive comments towards improvement of the original version of this paper.

Author information

Authors and Affiliations

  1. Faculty of Sciences and Mathematics, University of Niš, P.O. Box 224, 18000, Niš, Serbia

    Dijana Mosić

Authors
  1. Dijana Mosić
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dijana Mosić.

Additional information

Communicated by Lee See Keong.

The author is supported by the Ministry of Science, Republic of Serbia, Grant No. 174007.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mosić, D. Reflexive–EP Elements in Rings. Bull. Malays. Math. Sci. Soc. 40, 655–664 (2017). https://doi.org/10.1007/s40840-017-0445-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40840-017-0445-4

Keywords

Mathematics Subject Classification

Search

Navigation