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Year 2024, , 184 - 193, 12.07.2024

Bibi Roghaye Bahlakeh , Rahman Bahmani Sangesari , Marjan Sheibani Abdolyousefi , N. Ashrafi

https://doi.org/10.24330/ieja.1478635

Abstract

References

  • N. Castro Gonzalez and J. J. Koliha, New additive results for the g-Drazin inverse, Proc. Roy. Soc. Edinburgh Sect. A, 134 (2004), 1085-1097.
  • H. Chen and M. Sheibani, The g-Hirano inverse in Banach algebras, Linear Multilinear Algebra, 69 (2021), 1352-1362.
  • H. Chen and M. Sheibani, Jacobson's Lemma for the generalized n-strongly Drazin inverse, arXiv: 2001.00328v2 [math.RA].
  • D. S. Cvetkovic-Ilic, D. S. Djordjevic and Y. Wei, Additive results for the generalized Drazin inverse in a Banach algebra, Linear Algebra Appl., 418 (2006), 53-61.
  • D. S. Cvetkovic-Ilic, X. Liu and Y. Wei, Some additive results for the generalized Drazin inverse in a Banach algebra, Electron. J. Linear Algebra, 22 (2011), 1049-1058.
  • P. V. Danchev, A note on periodic rings, Vladikavkaz. Mat. Zh., 23(4) (2021), 109-111.
  • C. Deng, D. S. Cvetcovic-Ilic and Y. Wei, Some results on the generalized Drazin inverse of operator matrices, Linear Multilinear Algebra, 58 (2010), 503-521.
  • C. Deng and Y. Wei, New additive results for the generalized Drazin inverse, J. Math. Anal. Appl., 370 (2010), 313-321.
  • A. Diesl, Sums of commuting potent and nilpotent elements in rings, J. Algebra Appl., 22(5) (2023), 2350113 (33 pp).
  • A. Ghaffari, T. Haddadi and M. Sheibani Abdolyousefi, An extension of Hirano inverses in Banach algebras, Filomat, 36 (2022), 3197-3206.
  • D. Mosic, H. Zou and J. Chen, The generalized Drazin inverse of the sum in a Banach algebra, Ann. Funct. Anal., 8 (2017), 90-105.
  • H. Yang and X. Liu, The Drazin inverse of the sum of two matrices and its applications, J. Comput. Appl. Math., 235 (2011), 1412-1417.
  • H. Zou, T. Li and Y. Wei, On the g$\pi$-Hirano invertibility in Banach algebras, arXiv:2302.06080v1 [math.RA].
  • H. Zou, D. Mosic, K. Zuo and Y. Chen, On the n-strong Drazin invertibility in rings, Turkish J. Math., 43 (2019), 2659-2679.

Generalized $\pi$-Hirano inverses of the sum in Banach algebras

Year 2024, , 184 - 193, 12.07.2024

Bibi Roghaye Bahlakeh , Rahman Bahmani Sangesari , Marjan Sheibani Abdolyousefi , N. Ashrafi

https://doi.org/10.24330/ieja.1478635

Abstract

In this paper, we investigate some additive results on g$\pi$-Hirano invertibility in Banach algebras. By applying our results, some new results for operator matrices are obtained. This extends the main results of [H. Zou, T. Li and Y. Wei, arXiv:2302.06080v1].

Keywords

Drazin inverse g$\pi$-Hirano inverse additive property operator matrix spectral idempotent

References

  • N. Castro Gonzalez and J. J. Koliha, New additive results for the g-Drazin inverse, Proc. Roy. Soc. Edinburgh Sect. A, 134 (2004), 1085-1097.
  • H. Chen and M. Sheibani, The g-Hirano inverse in Banach algebras, Linear Multilinear Algebra, 69 (2021), 1352-1362.
  • H. Chen and M. Sheibani, Jacobson's Lemma for the generalized n-strongly Drazin inverse, arXiv: 2001.00328v2 [math.RA].
  • D. S. Cvetkovic-Ilic, D. S. Djordjevic and Y. Wei, Additive results for the generalized Drazin inverse in a Banach algebra, Linear Algebra Appl., 418 (2006), 53-61.
  • D. S. Cvetkovic-Ilic, X. Liu and Y. Wei, Some additive results for the generalized Drazin inverse in a Banach algebra, Electron. J. Linear Algebra, 22 (2011), 1049-1058.
  • P. V. Danchev, A note on periodic rings, Vladikavkaz. Mat. Zh., 23(4) (2021), 109-111.
  • C. Deng, D. S. Cvetcovic-Ilic and Y. Wei, Some results on the generalized Drazin inverse of operator matrices, Linear Multilinear Algebra, 58 (2010), 503-521.
  • C. Deng and Y. Wei, New additive results for the generalized Drazin inverse, J. Math. Anal. Appl., 370 (2010), 313-321.
  • A. Diesl, Sums of commuting potent and nilpotent elements in rings, J. Algebra Appl., 22(5) (2023), 2350113 (33 pp).
  • A. Ghaffari, T. Haddadi and M. Sheibani Abdolyousefi, An extension of Hirano inverses in Banach algebras, Filomat, 36 (2022), 3197-3206.
  • D. Mosic, H. Zou and J. Chen, The generalized Drazin inverse of the sum in a Banach algebra, Ann. Funct. Anal., 8 (2017), 90-105.
  • H. Yang and X. Liu, The Drazin inverse of the sum of two matrices and its applications, J. Comput. Appl. Math., 235 (2011), 1412-1417.
  • H. Zou, T. Li and Y. Wei, On the g$\pi$-Hirano invertibility in Banach algebras, arXiv:2302.06080v1 [math.RA].
  • H. Zou, D. Mosic, K. Zuo and Y. Chen, On the n-strong Drazin invertibility in rings, Turkish J. Math., 43 (2019), 2659-2679.
There are 14 citations in total.

Details

Primary Language English
Subjects Algebra and Number Theory
Journal Section Articles
Authors

Bibi Roghaye Bahlakeh

Rahman Bahmani Sangesari

Marjan Sheibani Abdolyousefi

N. Ashrafi This is me

Early Pub Date May 5, 2024
Publication Date July 12, 2024
Submission Date October 12, 2023
Acceptance Date February 15, 2024
Published in Issue Year 2024

Cite

APA Bahlakeh, B. R., Bahmani Sangesari, R., Sheibani Abdolyousefi, M., Ashrafi, N. (2024). Generalized $\pi$-Hirano inverses of the sum in Banach algebras. International Electronic Journal of Algebra, 36(36), 184-193. https://doi.org/10.24330/ieja.1478635
AMA Bahlakeh BR, Bahmani Sangesari R, Sheibani Abdolyousefi M, Ashrafi N. Generalized $\pi$-Hirano inverses of the sum in Banach algebras. IEJA. July 2024;36(36):184-193. doi:10.24330/ieja.1478635
Chicago Bahlakeh, Bibi Roghaye, Rahman Bahmani Sangesari, Marjan Sheibani Abdolyousefi, and N. Ashrafi. “Generalized $\pi$-Hirano Inverses of the Sum in Banach Algebras”. International Electronic Journal of Algebra 36, no. 36 (July 2024): 184-93. https://doi.org/10.24330/ieja.1478635.
EndNote Bahlakeh BR, Bahmani Sangesari R, Sheibani Abdolyousefi M, Ashrafi N (July 1, 2024) Generalized $\pi$-Hirano inverses of the sum in Banach algebras. International Electronic Journal of Algebra 36 36 184–193.
IEEE B. R. Bahlakeh, R. Bahmani Sangesari, M. Sheibani Abdolyousefi, and N. Ashrafi, “Generalized $\pi$-Hirano inverses of the sum in Banach algebras”, IEJA, vol. 36, no. 36, pp. 184–193, 2024, doi: 10.24330/ieja.1478635.
ISNAD Bahlakeh, Bibi Roghaye et al. “Generalized $\pi$-Hirano Inverses of the Sum in Banach Algebras”. International Electronic Journal of Algebra 36/36 (July 2024), 184-193. https://doi.org/10.24330/ieja.1478635.
JAMA Bahlakeh BR, Bahmani Sangesari R, Sheibani Abdolyousefi M, Ashrafi N. Generalized $\pi$-Hirano inverses of the sum in Banach algebras. IEJA. 2024;36:184–193.
MLA Bahlakeh, Bibi Roghaye et al. “Generalized $\pi$-Hirano Inverses of the Sum in Banach Algebras”. International Electronic Journal of Algebra, vol. 36, no. 36, 2024, pp. 184-93, doi:10.24330/ieja.1478635.
Vancouver Bahlakeh BR, Bahmani Sangesari R, Sheibani Abdolyousefi M, Ashrafi N. Generalized $\pi$-Hirano inverses of the sum in Banach algebras. IEJA. 2024;36(36):184-93.