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)].
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References
C. Bu, K. Zhang, and J. Zhao, “Representation of the Drazin inverse on solution of a class singular differential equations,” Linear Multilinear Algebra 59, 863–877 (2011).
A. Shakoor, I. Ali, S. Wali, and A. Rehman, “Some formulas on the Drazin inverse for the sum of two matrices and block matrices,” Bull. Iran. Math. Soc. 48 (2), 351–366 (2022).
H. Yang and X. Liu, “The Drazin inverse of the sum of two matrices and its applications,” J. Comput. Applied Math. 235, 1412–1417 (2011).
R. Yousefi and M. Dana, “Generalizations of some conditions for Drazin inverses of the sum of two matrices,” Filomat 32, 6417–6430 (2018).
H. Zou, D. Mosić, and Y. Chen, “The existence and representation of the Drazin inverse of a \(2\times 2\) block matrix over a ring,” J. Algebra Appl. 18 (11) (2019) Article ID 1950212.
M. Dana and R. Yousefi, “Formulas for the Drazin inverse of matrices with new conditions and its applications,” Int. J. Appl. Comput. Math. 4 (1) (2018) Paper No.4.
E. Dopazo and M. F. Martinez-Serrano, “Further results on the representation of the Drazin inverse of a \(2\times 2\) block matrix,” Linear Algebra Appl. 432, 1896–1904 (2010).
A. Yu, X. Wang, and C. Deng, “On the Drazin inverse of an anti-triangular block matrix,” Linear Algebra Appl. 489, 274–287 (2016).
D. Zhang and D. Mosić, “Explicit formulae for the generalized Drazin inverse of block matrices over a Banach algebra,” Filomat 32 (17), 5907–5917 (2018).
L. Xia and B. Deng, “The Drazin inverse of the sum of two matrices and its applications,” Filomat 31, 5151–5158 (2017).
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Chen, H., Sheibani, M. The g-Drazin Invertibility of a Block Operator Matrix. Math Notes 114, 1163–1168 (2023). https://doi.org/10.1134/S0001434623110482
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DOI: https://doi.org/10.1134/S0001434623110482