Abstract
In this note, we investigate the existence of the Drazin inverse for the anti-triangular operator matrix \(M= \left( {\begin{matrix} A &{} B \\ C &{} 0 \end{matrix}}\right) \) with \(A^2=A\) and \( CAB=0\), and the explicit representation of \(M^D\) is given in term of \(A, A^D, B,C \) and \((CB)^D\). In addition, it is shown that \(\mathrm {ind} (M)\le 2 \ \mathrm {ind} (CB)+2\), which is important to prove the existence and representation of the Drazin inverse for M.
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Communicated by Poom Kumam.
This work is supported by the NNSF of China (Nos. 11261034 and 11461049), and the NSF of Inner Mongolia (No. 2017MS0118).
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Wang, H., Wu, C. & Huang, J. Drazin Inverse of Anti-triangular Operator Matrices. Bull. Malays. Math. Sci. Soc. 42, 1071–1083 (2019). https://doi.org/10.1007/s40840-017-0533-5
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DOI: https://doi.org/10.1007/s40840-017-0533-5