Developing reverse order law for the Moore-Penrose inverse with the product of three linear operators
type: Item
instance of: scholarly article
title: Developing reverse order law for the Moore-Penrose inverse with the product of three linear operators
zbMATH Open document ID: 1477.15002
DOI: 10.1155/2021/6585951
author: Yang Qi
author: Liu Xiaoji
author: Yu Yaoming
published in: Journal of Mathematics
publication date: 2021-11-24T00:00:00Z
review text: Summary: In this paper, we study the reverse order law for the Moore-Penrose inverse of the product of three bounded linear operators in Hilbert spaces. We first present some equivalent conditions for the existence of the reverse order law \((ABC)^\dagger= C^\dagger B^\dagger A^\dagger\). Moreover, several equivalent statements of \(\mathscr{R}(AA^\ast (ABC))=\mathscr{R}(ABC)\) and \(\mathscr{R}(C^\ast C(ABC)^\ast)=\mathscr{R}((ABC)^\ast)\) are also deducted by the theory of operators.
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 7433089
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/6585951
OpenAlex ID: W3210608742
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description: scientific article; zbMATH DE number 7433089