Invertible completions of 2×2 upper triangular operator matrices

In this note we prove that if M C = ( A a m p ; C 0 a m p ; B ) \begin{equation*}M_{C}=\left (\begin {smallmatrix}A&C\ 0&B\end{smallmatrix} \right ) \end{equation*} is a 2 × 2 2\times 2 upper triangular operator matrix acting on the Banach space X ⊕ Y X\oplus Y , then M C M_{C} is invertible for som... View More