# Consistency in invertibility and Fredholmness of operator matrices

### Dragana S. Cvetković-Ilić

University of Niš, Serbia### Marko Kostadinov

University of Niš, Serbia

## Abstract

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?

## Cite this article

Dragana S. Cvetković-Ilić, Marko Kostadinov, Consistency in invertibility and Fredholmness of operator matrices. J. Spectr. Theory 9 (2019), no. 2, pp. 635–649

DOI 10.4171/JST/258