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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
2519-9269 (Print)
2519-9277 (Online)
Volume 1
Issue 1
2016
August
0
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
32
38
English
Hanifa ZekraouiFaculty of Exact and Natural Sciences, Department of Mathematics
University L’Arbi Ben M’hidi BP 358, Oum-El-Bouaghi 04000, Algeria
hanifazekraoui@yahoo.fr
Cenap OzelFaculty of Sciences, Department of MathematicsDokuz Eylul University, Tinaztepe Kampus 35160, Buca, izmir, Turkey, and,Faculty of Sciences, Department of MathematicsKing Abdulaziz University, KAU 21589, Jeddah, Saudi Arabia.
cenap.ozel@gmail.com
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.
Generalized inverse; Moore-Penrose inverse; reverse order law; norm majorization; factorization; Hilbert space.
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