G-Drazin inverse and group inverse for the anti-triangular block-operator matrices

Huanyin Chen, Marjan Sheibani

We present the generalized Drazin inverse for certain anti-triangular operator matrices. Let $E,F,E{F}^{\pi }\in \mathcal{B}(X{)}^d$. If $EFE{F}^{\pi }=0$ and $F^{2}E{F}^{\pi }=0$, we prove that $M=\left(…