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#### Article Title

#### Keywords

Invertibility, Operator matrix, Regularity, Inner inverse.

#### Abstract

In this paper, for given operators A ∈ B(X) and B ∈ B(Y), the set of all C ∈ B(Y,X) such that the operator matrix M_C = \left[ \begin{array}{cc} A & C \\ O & B \end{array} \right] is injective, invertible, left invertible and right invertible, is described. Answers to some open questions are given. Also, in the case when A and B are relatively regular operators, the set of all C ∈ B(Y,X) such that M_C is regular is described. In addition, a necessary and a sufficient conditions are given for MC to be regular with the inner inverse of a certain given form.

#### Recommended Citation

Cvetkovic-Ilic, Dragana S..
(2015),
"Invertible and regular completions of operator matrices",
*Electronic Journal of Linear Algebra*,
Volume 30, pp. 530-549.

DOI: http://dx.doi.org/10.13001/1081-3810.3126

*Abstract*