Invertibility of Operator Matrices on a Banach Space |
| |
Authors: | Guojun Hai Alatancang Chen |
| |
Institution: | 1. School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, People’s Republic of China
|
| |
Abstract: | Let $\mathcal X $ and $\mathcal Y $ be Banach spaces, and let $A\in \mathcal B (\mathcal X )$ and $C\in \mathcal B (\mathcal Y , \mathcal X )$ be given operators. A necessary and sufficient condition is given for $\left \begin{array}{cc} A&C \\ X&Y \\ \end{array} \right]$ to be invertible (respectively, left invertible) for some $X\in \mathcal B (\mathcal X , \mathcal Y )$ and $Y\in \mathcal B (\mathcal Y )$ . Furthermore, some related results are obtained. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|