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arXiv · 2209.13835

The g-Drazin inverses of anti-triangular block operator matrices

Huanyin Chen·Marjan Sheibani
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Abstract

An element $a$ in a Banach algebra $\mathcal{A}$ has g-Drazin inverse if there exists $b\in \mathcal{A}$ such that $ab=ba, b=bab$ and $a-a^2b \in \mathcal{A}^{qnil}$. In this paper we find new explicit representations of the g-Drazin inverse of the block operator matrix $\left( \begin{array}{cc} E&I F&0 \end{array} \right)$. We thereby solve a wider kind of singular differential equations posed by Campbell [S.L. Campbell, The Drazin inverse and systems of second order linear differential equations, Linear $\&$ Multilinear Algebra, 14(1983), 195--198].

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Huanyin Chen, Marjan Sheibani. 2022-09-28. The g-Drazin inverses of anti-triangular block operator matrices. https://arxiv.org/abs/2209.13835

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