On the generalized Drazin-Riesz inverse for closed linear operators
type: Item
instance of: scholarly article
title: On the generalized Drazin-Riesz inverse for closed linear operators
zbMATH Open document ID: 1501.47001
author: Othman Abad
author: H. Zguitti
published in: Mediterranean Journal of Mathematics
publication date: 2022-01-27T00:00:00Z
review text: Let \(X\) be a complex Banach space, \(B(X)\) stand for the space of bounded linear operators, and \(C(X)\) denote the space of closed linear operators, on \(X\), respectively. Let \(R(.)\) and \(D(.)\) denote the range space and the domain space, respectively. \(A \in C(X)\) is said to be generalized Drazin-Riesz invertible if there exists \(B\in B(X)\) such that the following are satisfied: \(R(B) \subseteq D(A)\), \(R(I-AB) \subseteq D(A)\), \(AB=BA\), \(BAB=B\), and the operator \(A(I-AB)\) is bounded Riesz. In this paper, some of the basic results on Drazin invertibility of bounded operators are extended to closed linear operators.
reviewed by: K. C. Sivakumar
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 47B06
zbMATH DE Number: 7465522
zbMATH Keywords: closed Drazin operator
zbMATH Keywords: closed Browder operator
zbMATH Keywords: Riesz operators
MaRDI profile type: Publication
full work available at URL: s00009-021-01967-3
OpenAlex ID: W4207079196
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DOI: 10.1007/S00009-021-01967-3
description: scientific article; zbMATH DE number 7465522