The invertibility of 2X2 operator matrices
  In this paper the properties of right invertible row operators, i.e., of 1X2 surjective operator matrices are studied. This investigation is based on a specific space decomposition. Using this decomposition, we characterize the invertibility of a 2X2 operator matrix. As an application, the invertibility of Hamiltonian operator matrices is investigated. 
Junjie Huang, Junfeng Sun, Alatancang Chen, Carsten Trunk
math.FA math.SP