Group inverse, Block operator matrix, EP operator
The main topic of this paper is the group invertibility of operators in Hilbert spaces. Conditions for the existence of the group inverses of products of two operators and the group invertibility of anti-triangular block operator matrices are studied. The equivalent conditions related to the reverse order law for the group inverses of operators are obtained.
"On the group invertibility of operators",
Electronic Journal of Linear Algebra,
Volume 31, pp. 492-510.