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New results on reverse order law for $ \{1,2,3\}$- and $ \{1,2,4\}$-inverses of bounded operators

Authors: Xiaoji Liu, Shuxia Wu and Dragana S. Cvetković-Ilić
Journal: Math. Comp. 82 (2013), 1597-1607
MSC (2010): Primary 15A09
Published electronically: January 11, 2013
MathSciNet review: 3042577
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Abstract: In this paper, using some block-operator matrix techniques, we give necessary and sufficient conditions for the reverse order law to hold for $ \{1,2,3\}$- and $ \{1,2,4\}$-inverses of bounded operators on Hilbert spaces. Furthermore, we present some new equivalents of the reverse order law for the Moore-Penrose inverse.

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Additional Information

Xiaoji Liu
Affiliation: College of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning 530006, People’s Republic of China

Shuxia Wu
Affiliation: College of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning 530006, People’s Republic of China

Dragana S. Cvetković-Ilić
Affiliation: University of Niš, Department of Mathematics, Faculty of Sciences and Mathematics, 18000 Niš, Serbia

Keywords: Block-operator matrix, Moore-Penrose inverse, reverse order law, ${1,2,3}$-inverse, ${1, 2, 4}$-inverse
Received by editor(s): April 22, 2011
Received by editor(s) in revised form: November 9, 2011
Published electronically: January 11, 2013
Additional Notes: This work ws supported by Grant No. 174007 of the Ministry of Science, Technology and Development, Republic of Serbia
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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