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Journal of Spectral Theory

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Volume 9, Issue 2, 2019, pp. 635–649
DOI: 10.4171/JST/258

Published online: 2018-10-24

Consistency in invertibility and Fredholmness of operator matrices

Dragana S. Cvetković-Ilić[1] and Marko Kostadinov[2]

(1) University of Niš, Serbia
(2) University of Niš, Serbia

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?

Keywords: Consistency, consistent in invertibility, Fredholm operator, Fredholm consistent operator, operator matrices

Cvetković-Ilić Dragana, Kostadinov Marko: Consistency in invertibility and Fredholmness of operator matrices. J. Spectr. Theory 9 (2019), 635-649. doi: 10.4171/JST/258