Frames Containing a Riesz Basis and Approximation of the Frame Coefficients Using Finite-Dimensional Methods

We consider frames which contain a Riesz basis. Among those, we find Riesz frames, i.e., frames with the property that every subfamily is a frame for its closed linear span, with a common lower bound. We point out the connection to the projection method, which can be used to approximate the frame coefficients for a Riesz frame using finitely many elements of the frame. Under different conditions we show that the projection method even approximates the frame coefficient in l 2-sense.