Projection methods for inversion of unbounded operators

Let T be a closed linear operator defined on a dense subspace D(T) of a separable complex Hilbert space H and suppose that T has a bounded inverse. We characterize the convergence of projection methods for solving the operator equation Tx = y. We discuss the stability of convergence of projection methods under bounded perturbations. Also we discuss convergence of modified projection methods. We give examples to illustrate our results.