Operator matrix of Moore–Penrose inverse operators on Hilbert C*-modules
Mehdi Mohammadzadeh Karizaki, Mahmoud Hassani, Maryam Amyari, Maryam Khosravi · Colloquium Mathematicum · 2015
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 $