THE INVERSE OF OPERATOR MATRIX A WHERE A≥I

Abstract

Let H and K be Hilbert spaces and let H K be the cartesian product of them.Let
B(H),B(K),B(H  K),B(K,H),B(H,K) be the Banach spaces of bounded(continuous)
operators on H,K,H K,and from K into H and from H into K respectively. In this
paper we find the inverse of operator matrix





D E
B C
A B(H K) where
BB(H) ,CB(K,H), DB(H,K), EB(K) and A≥ H K I  where H K I  is the
identity operator on H K.