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.
MSC 2010: 47A05 : Operator theory / General theory of linear operators / General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 47A10 : Operator theory / General theory of linear operators / Spectrum, resolvent