The inverse of operator matrix A where A≥I and A

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 matrixB(H⊕K) where BÑ”B(H) ,CÑ”B(K,H), DÑ”B(H,K), EÑ”B(K) and A≥ , Awhere  is the identity operator on H⊕K