Skip to main content
SpringerLink
Log in

Weighted extended g-Drazin inverse

  • Published:
Aequationes mathematicae Aims and scope Submit manuscript

Abstract

We define a weighted extended g-Drazin inverse for Banach algebra elements, generalizing the concepts of extended g-Drazin inverse and weighted g-Drazin inverse. We characterize weighted extended g-Drazin invertible elements and present some representations of a weighted extended g-Drazin inverse. Applying these results, we introduce and investigate a weighted extended Drazin 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. Ben-Israel, A., Greville, T.N.E.: Generalized Inverses: Theory and Applications, 2nd edn. Springer, Berlin (2003)

    MATH  Google Scholar 

  2. Cline, R.E., Greville, T.N.E.: A Drazin inverse for rectangular matrices. Linear Algebra Appl. 29, 53–62 (1980)

    Article  MathSciNet  Google Scholar 

  3. Dajić, A., Koliha, J.J.: The weighted g-Drazin inverse for operators. J. Aust. Math. Soc. 82, 163–181 (2007)

    Article  MathSciNet  Google Scholar 

  4. Drazin, M.P.: Pseudo-inverses in associate rings and semigroups. Am. Math. Mon. 65, 506–514 (1958)

    Article  Google Scholar 

  5. Hernández, A., Lattanzi, M., Thome, N.: On some new pre-orders defined by weighted Drazin inverses. Appl. Math. Comput. 282, 108–116 (2016)

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. Kyrchei, I.: Determinantal representations of the W-weighted Drazin inverse over the quaternion skew field. Appl. Math. Comput. 264, 453–465 (2015)

    MathSciNet  MATH  Google Scholar 

  8. Mosić, D.: Extended g-Drazin inverse in a Banach algebra. Bull. Malays. Math. Sci. Soc. (2019). https://doi.org/10.1007/s40840-019-00722-y

    Article  MATH  Google Scholar 

  9. Mosić, D.: Reverse order laws for the generalized Drazin inverse in Banach algebras. J. Math. Anal. Appl. 429(1), 461–477 (2015)

    Article  MathSciNet  Google Scholar 

  10. Mosić, D.: Weighted binary relations for operators on Banach spaces. Aequat. Math. 90(4), 787–798 (2016)

    Article  MathSciNet  Google Scholar 

  11. Mosić, D.: Weighted pre-orders in a Banach algebra. Linear Algebra Appl. 533, 161–185 (2017)

    Article  MathSciNet  Google Scholar 

  12. Mosić, D., Djordjević, D.S.: Weighted generalized Drazin inverse in rings. Georgian Math. J. 23(4), 587–594 (2016)

    Article  MathSciNet  Google Scholar 

  13. Stanimirović, P.S., Katsikis, V.N., Ma, H.: Representations and properties of the W-weighted Drazin inverse. Linear Multilinear Algebra 65(6), 1080–1096 (2017)

    Article  MathSciNet  Google Scholar 

  14. Rakočević, V., Wei, Y.: A weighted Drazin inverse and applications. Linear Algebra Appl. 350(1–3), 25–39 (2002)

    Article  MathSciNet  Google Scholar 

  15. Rakočević, V., Wei, Y.: The representation and approximation of the W-weighted Drazin inverse of linear operators in Hilbert space. Appl. Math. Comput. 141, 455–470 (2003)

    MathSciNet  MATH  Google Scholar 

  16. Wang, X.Z., Ma, H., Stanimirović, P.S.: Recurrent neural network for computing the W-weighted Drazin inverse. Appl. Math. Comput. 300, 1–20 (2017)

    MathSciNet  MATH  Google Scholar 

  17. Wei, Y.: Integral representation of the W-weighted Drazin inverse. Appl. Math. Comput. 144(1), 3–10 (2003)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Dijana Mosić

  2. School of Mathematical Sciences, Yangzhou University, Yangzhou, 225002, China

    Long Wang

Authors
  1. Dijana Mosić
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Long Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dijana Mosić.

Additional information

Publisher's Note

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

The first author is supported by the Ministry of Education, Science and Technological Development, Republic of Serbia, Grant No. 174007. The second author is supported by the NSFC (11871063), NSF of Jiangsu Province (BK20170589), NSF of Jiangsu Higher Education Institutions of China (15KJB110021), China Postdoctoral Science Foundation Funded Project (2017M611920).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mosić, D., Wang, L. Weighted extended g-Drazin inverse. Aequat. Math. 94, 151–161 (2020). https://doi.org/10.1007/s00010-019-00656-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00010-019-00656-7

Keywords

Mathematics Subject Classification

Search

Navigation