General Letters in Mathematics

Volume 1 - Issue 1 (4) | PP: 32 - 38 Language : English
DOI : https://doi.org/DOI:10.31559/glm2016.1.1.4
613
82

The Invariance of the Reverse Order Law under Generalized Inverses of the Product of Two Closed Range Bounded Linear Operators on Hilbert Spaces and Characterization of the Property by the Norm Majorization

Hanifa Zekraoui ,
Cenap Ozel
Received Date Revised Date Accepted Date Publication Date
25/5/2016 29/6/2016 18/7/2016 30/8/2016
Abstract
In this paper we extend the invariance of the product AC B under a generalized inverse C of a matrix C in finite dimensional vector spaces to the Hilbert spaces by using Douglas’s theorem, then we investigate the result and results of the reverse order on Hilbert spaces to study the equivalent conditions for the invariance of the property of the reverse order law for the product of two closed range linear bounded operators on Hilbert spaces. Then, we characterize the property by the norm majorization.


How To Cite This Article
Zekraoui , H. & Ozel , C. (2016). The Invariance of the Reverse Order Law under Generalized Inverses of the Product of Two Closed Range Bounded Linear Operators on Hilbert Spaces and Characterization of the Property by the Norm Majorization . General Letters in Mathematics, 1 (1), 32-38, DOI:10.31559/glm2016.1.1.4

Copyright © 2024, This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.