Quasi-diagonality and the finite section method

Abstract

Quasi-diagonal operators on a Hilbert space are a large and important class (containing all self-adjoint operators for instance). They are also perfectly suited for study via the finite section method (a particular Galerkin method). Indeed, the very definition of quasi-diagonality yields finite sections with good convergence properties. Moreover, simple operator theory techniques yield estimates on certain rates of convergence. In the case of quasi-diagonal band operators both the finite sections and rates of convergence are explicitly given.