Moore-Penrose inverse of Gram operator on Hilbert C*-modules
Abstract
Let
t
be a regular operator between Hilbert
C
∗
-modules and
t
†
be its Moore-Penrose inverse. We investigate the Moore-Penrose invertibility of the Gram operator
t
∗
t
. More precisely, we study some conditions ensuring that
t
†
=(
t
∗
t
)
†
t
∗
=
t
∗
(t
t
∗
)
†
and
(
t
∗
t
)
†
=
t
†
t
∗†
hold. As an application, we get some results for densely defined closed operators on Hilbert
C
∗
-modules over
C
∗
-algebras of compact operators.