Abstract
We establish some triple reverse order laws for the generalized Drazin inverse and then obtain from one of them various expressions of the generalized Drazin inverse of a block matrix in a Banach algebra.
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Benítez J., Thome N.: The generalized Schur complement in group inverses and (k + 1)-potent matrices. Linear Multilinear Algebr. 54, 405–413 (2006)
Campbell S.L., Meyer C.D.: Generalized Inverses of Linear Transformations. Pitman, London (1979)
Castro-González N., Koliha J.J.: New additive results for the g-Drazin inverse. Proc. Roy. Soc. Edinburgh Sect. A 134, 1085–1097 (2004)
Castro-González N., Martínez-Serrano M.F.: Drazin inverse of partitioned matrices in terms of Banachiewicz-Schur forms. Linear Algebr. Appl. 432, 1691–1702 (2010)
Deng C., Wei Y.: Representations for the Drazin inverse of 2 × 2 block-operator matrix with singular Schur complement. Linear Algebr. Appl. 435, 2766–2783 (2011)
Djordjević D.S., Wei Y.: Additive results for the generalized Drazin inverse. J. Austral. Math. Soc. 73, 115–125 (2002)
Hartwig R.E., Li X., Wei Y.: Representations for the Drazin inverse of 2 × 2 block matrix. SIAM J. Matrix Anal. Appl. 27, 757–771 (2006)
Koliha J.J.: A generalized Drazin inverse. Glasgow Math. J. 38, 367–381 (1996)
Mosić D., Djordjević D.S.: Reprezentation for the generalized Drazin inverse of block matrices in Banach algebras. Appl. Math. Comput. 218, 12001–12007 (2012)
Zhao, L.: The Expression of the Drazin Inverse with Rank Constraints, J. Appl. Math. (390592), 10 (2012). doi:10.1155/2012/390592
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The author is supported by the Ministry of Education and Science, Republic of Serbia, Grant No. 174007.
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Mosić, D. The generalized Drazin inverse of a block matrix in a Banach algebra. Aequat. Math. 89, 849–855 (2015). https://doi.org/10.1007/s00010-014-0280-8
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DOI: https://doi.org/10.1007/s00010-014-0280-8