Representations for generalized Drazin inverse of operator matrices over a Banach space

TL;DR

This paper derives formulas for the generalized Drazin inverse of specific operator matrices over Banach spaces, unifying and extending previous results in the literature.

Contribution

It provides new expressions for the generalized Drazin inverse of (2,2,0) and 2x2 operator matrices, broadening existing theoretical frameworks.

Findings

Derived formulas for the generalized Drazin inverse of (2,2,0) operator matrices.

Unified and extended previous results in the literature.

Applicable under certain conditions to generalize known cases.

Abstract

In this paper we give expressions for the generalized Drazin inverse of a (2,2,0) operator matrix and a $2\times2$ operator matrix under certain circumstances, which generalizes and unifies several results in the literature.