论文标题
抗三角块操作员矩阵的G-德拉津逆逆
The g-Drazin inverses of anti-triangular block operator matrices
论文作者
论文摘要
如果存在$ b \，则banach代数$ \ mathcal {a} $在\ mathcal {a} $中存在$ b \ ab = ba = ba = b = bab = $和$ a-a-a^2b \ in \ Mathcal {a}^{qnil} $。在本文中，我们发现块操作员矩阵$ \ left的G-Drazin倒数的新明确表示（ \ begin {array} {cc} E＆I F＆0 \ end {array} \ right）$。因此，我们解决了坎贝尔[S.L.坎贝尔，Drazin逆和二阶线性微分方程的系统，线性$ \＆$多连线代数，14（1983），195---198]。
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].
