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Matematicheskie Zametki, 2023, Volume 114, Issue 6, paper published in the English version journal (Mi mzm14274)  
The $g$-Drazin Invertibility of a Block Operator Matrix

Huanyin Chena, Marjan Sheibanib

a School of Big Data, Fuzhou University of International Studies and Trade, Fuzhou, 350202, China
b Farzanegan Campus, Semnan University, Semnan, 55798-35146, Iran
Abstract: We present new additive properties of the $g$-Drazin inverse of a linear operator on a Banach space. The $g$-Drazin invertibility of certain $2\times 2$ block operator matrices on a Banach space is thereby established. These results extend many known results, e.g., by Yang and Liu [J. Comput. Applied Math. 235, 1412–1417 (2011)] and Dopazo and Martinez-Serrano [Linear Algebra Appl. 432, 1896–1904 (2010)].
Keywords: $g$-Drazin inverse, Cline's formula, spectral idempotent, block operator matrix, Banach space.
Funding agency
This work was supported by ongoing institutional funding.
Received: 23.05.2022
Revised: 16.10.2023
English version:
Mathematical Notes, 2023, Volume 114, Issue 6, Pages 1163–1168
DOI: https://doi.org/10.1134/S0001434623110482
Bibliographic databases:
Document Type: Article
Language: English
Citation: Huanyin Chen, Marjan Sheibani, “The $g$-Drazin Invertibility of a Block Operator Matrix”, Math. Notes, 114:6 (2023), 1163–1168
Citation in format AMSBIB
\Bibitem{CheShe23}
\by Huanyin~Chen, Marjan~Sheibani
\paper The $g$-Drazin Invertibility of a Block Operator Matrix
\jour Math. Notes
\yr 2023
\vol 114
\issue 6
\pages 1163--1168
\mathnet{http://mi.mathnet.ru/mzm14274}
\crossref{https://doi.org/10.1134/S0001434623110482}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85187694408}
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