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Operator matrix of Moore-Penrose inverse operators on Hilbert C*-modules

Mehdi Mohammadzadeh Karizaki;  Mahmoud Hassani;  Maryam Amyari;  Maryam Khosravi — 2015

Colloquium Mathematicae

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.

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