Quasi-orthogonal decompositions of structured frames

A decomposition of a Hilbert space Hscr; into a quasi-orthogonal family of closed subspaces is introduced. We shall investigate conditions in order to derive bounded families of corresponding quasi-projectors or resolutions of the identity operator. Given a local family of atoms, or generalized stable basis, for each subspace, we show that the union of the local atoms can generate a global frame for the Hilbert space. Corresponding duals can be calculated in a flexible way by means of systems of quasi-projectors. An application to Gabor frames is presented as example of the use of this technique, for calculation of duals and explicit estimates of lattice constants.