The G-Drazin inverse of anti-triangular block-operator matrices

Year 2024, Early Access, 1 - 8

F. Zamiri, A. Ghaffari Marjan Sheibani Abdolyousefi

https://doi.org/10.24330/ieja.1587216

Abstract

In this paper we investigate the g-Drazin invertibility of an anti-triangular block-operator matrix $\left(
\begin{array}{cc}
E&I\\
F&0
\end{array}
\right)$ with $F^{\pi}EF^d=0$ and $F^{\pi}EF^iE=0$ for all $i\in {\mathbb N}$. This generalizes the main results of [Guo, Zou and Chen, Hacet. J. Math. Stat., 49(3)(2020), 1134-1149] and [Chen and Sheibani, Appl. Math. Comput., 463(2024), 128368 (12 pp)] to a wider case.

Keywords

g-Drazin inverse, block-operator matrix, bounded linear operator, spectral idempotent

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