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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

Volume 1, Issue 1, Article 4 - 2016

Authors: Hanifa Zekraoui;Cenap Ozel

Copyright © 2016 . 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.

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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

@article{Zekraoui_2016, doi = {10.31559/glm2016.1.1.4}, url = {https://doi.org/10.31559%2Fglm2016.1.1.4}, year = 2016, month = {aug}, publisher = {Refaad for Studies and Research}, volume = {1}, number = {1}, author = {Hanifa Zekraoui and Cenap Ozel}, title = {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}, journal = {General Letters in Mathematics} }
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). doi:10.31559/glm2016.1.1.4
[1]H. Zekraoui and C. Ozel, “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, vol. 1, no. 1, Aug. 2016.
Zekraoui, Hanifa, and Cenap Ozel. “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, no. 1 (August 1, 2016). doi:10.31559/glm2016.1.1.4.