Left and right Drazin invertibility of operator matrices

Document Type : Original Article

Author

Kouider Miloud Hocine

Departement of mathematics, Faculty of mathematics and informatique, University of Sciences and Technology of Oran, Mohammed Boudiaf, USTO, Oran, Algeria.

10.22034/kjm.2023.377073.2729

Abstract

When $A \in \mathcal B(H)$ and $B \in \mathcal B(K) $ are given, we denote by $M_C$ the operator on the Hilbert space $H \oplus K$ of the form $M_C=\left( \begin{array}{ccc}
A & C \\
0 & B
\end{array} \right)$. In this paper, the closedness of ranges and left (resp. right) Drazin invertibility of upper triangular operator matrices $M_C$ are investigated.

Keywords

Bounded operators

range

left Drazin invertible operators

right Drazin invertible operators

operator matrix

Subjects

• 47 Operator theory

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