Operator matrix of Moore–Penrose inverse operators on Hilbert $C^*$-modules
Tom 140 / 2015
Colloquium Mathematicum 140 (2015), 171-182
MSC: Primary 46L08; Secondary 15A09, 47A05.
DOI: 10.4064/cm140-2-2
Streszczenie
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.
