Consistency in invertibility and Fredholmness of operator matrices
Dragana S. Cvetković‐Ilić, Marko Kostadinov · Journal of Spectral Theory · 2018
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{array}{cc} A & C \\ T & S \\ \end{array} } \right] is consistent in invertibility and Fredholmness?