Geodesic
Operator matrix of Moore–Penrose inverse operators on Hilbert $C^*$-modules
Mehdi Mohammadzadeh Karizaki1 ; Mahmoud Hassani1 ; Maryam Amyari1 ; Maryam Khosravi2
1 Department of Mathematics Mashhad Branch, Islamic Azad University Mashhad 91735, Iran
2 Faculty of Mathematics and Computer Science Shahid Bahonar University of Kerman Kerman, Iran and Tusi Mathematical Research Group (TMRG) P.O. Box 1113 Mashhad 91775, Iran
Colloquium Mathematicum, Tome 140 (2015) no. 2, pp. 171-182.

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We show that the Moore–Penrose inverse of an operator $T$ is idempotent if and only if it is a product of two projections. Furthermore, if $P$ and $Q$ are two projections, we find a relation between the entries of the associated operator matrix of $PQ$ and the entries of associated operator matrix of the Moore–Penrose inverse of $PQ$ in a certain orthogonal decomposition of Hilbert $C^*$-modules.
DOI : 10.4064/cm140-2-2
Keywords: moore penrose inverse operator idempotent only product projections furthermore projections relation between entries associated operator matrix entries associated operator matrix moore penrose inverse certain orthogonal decomposition hilbert * modules

Mehdi Mohammadzadeh Karizaki 1 ; Mahmoud Hassani 1 ; Maryam Amyari 1 ; Maryam Khosravi 2

1 Department of Mathematics Mashhad Branch, Islamic Azad University Mashhad 91735, Iran
2 Faculty of Mathematics and Computer Science Shahid Bahonar University of Kerman Kerman, Iran and Tusi Mathematical Research Group (TMRG) P.O. Box 1113 Mashhad 91775, Iran 
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Mehdi Mohammadzadeh Karizaki; Mahmoud Hassani; Maryam Amyari; Maryam Khosravi. Operator matrix of Moore–Penrose inverse operators on Hilbert $C^*$-modules. Colloquium Mathematicum, Tome 140 (2015) no. 2, pp. 171-182. doi : 10.4064/cm140-2-2. http://geodesic.mathdoc.fr/articles/10.4064/cm140-2-2/

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