The generalized Drazin inverse of operator matrices
- 2 June 2020
- journal article
- research article
- Published by Hacettepe University in Hacettepe Journal of Mathematics and Statistics
- Vol. 49 (3), 1134-1149
- https://doi.org/10.15672/hujms.731518
Abstract
Representations for the generalized Drazin inverse of an operator matrix $\begin{pmatrix} A & B\\C& D \end{pmatrix}$ are presented in terms of $A,B,C,D$ and the generalized Drazin inverses of $A,D,$ under the condition that $BD^d = 0$, and $BD_iC = 0$, for any nonnegative integer i. Using the representation, we give a new additive result of the generalized Drazin inverse for two bounded linear operators $P,Q \in B(X)$ with $PQ^d = 0$ and $PQ_iP = 0$, for any integer $ i \geqslant 1$. As corollaries, several well-known results are generalized
Keywords
This publication has 29 references indexed in Scilit:
- On Drazin inverse of operator matricesJournal of Mathematical Analysis and Applications, 2011
- The Drazin inverse of the sum of two matrices and its applicationsJournal of Computational and Applied Mathematics, 2011
- Some results on the generalized Drazin inverse of operator matricesLinear and Multilinear Algebra, 2009
- A note on the Drazin inverses with Banachiewicz–Schur formsApplied Mathematics and Computation, 2009
- Additive results for the generalized Drazin inverse in a Banach algebraLinear Algebra and its Applications, 2006
- Additive results for the generalized Drazin inverseJournal of the Australian Mathematical Society, 2002
- Some additive results on Drazin inverseLinear Algebra and its Applications, 2001
- A generalized Drazin inverseGlasgow Mathematical Journal, 1996
- Group inverses and Drazin inverses of bidiagonal and triangular Toeqlitz matricesJournal of the Australian Mathematical Society, 1977
- Pseudo-Inverses in Associative Rings and SemigroupsThe American Mathematical Monthly, 1958