On the inverse of a special Schur complement of an operator
Jovana Nikolov Radenković · Georgian Mathematical Journal · 2016
Abstract In this paper, we present various forms of the inverse of a special Schur complement C D - 1 B {CD^{-1}B} in the case where B, C, D are operators on Hilbert spaces. We show that when C D - 1 B {CD^{-1}B} is invertible, there always exist operators X and Y which belong to some special classes of generalized inverses of B and C, for which ( C D - 1 B ) - 1 = X D Y {(CD^{-1}B)^{-1}=XDY} . Some explicit expressions for such X and Y are given.