Consistency in invertibility and Fredholmness of operator matrices (Q2422545)

Summary: In this paper we completely answer the following question: for given \(A \in \mathcal B(\mathcal H,\mathcal K), C \in \mathcal B(\mathcal H,\mathcal K)\) does there exist operators \(T \in \mathcal B(\mathcal H,\mathcal L)\) and \(S \in \mathcal B(\mathcal K)\)such that the operator \(\left[ \begin{matrix} A C \\ T S \end{matrix} \right]\) is consistent in invertibility and Fredholmness?