Operator matrix of Moore–Penrose inverse operators on Hilbert $C^*$-modules
Colloquium Mathematicum, Tome 140 (2015) no. 2, pp. 171-182
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
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
Affiliations des auteurs :
Mehdi Mohammadzadeh Karizaki 1 ; Mahmoud Hassani 1 ; Maryam Amyari 1 ; Maryam Khosravi 2
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author = {Mehdi Mohammadzadeh Karizaki and Mahmoud Hassani and Maryam Amyari and Maryam Khosravi},
title = {Operator matrix of {Moore{\textendash}Penrose} inverse operators on {Hilbert} $C^*$-modules},
journal = {Colloquium Mathematicum},
pages = {171--182},
publisher = {mathdoc},
volume = {140},
number = {2},
year = {2015},
doi = {10.4064/cm140-2-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm140-2-2/}
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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
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