Frames and their associated H-F(p)-subspaces

Given a frame F = {f(j)} for a separable Hilbert space H, we introduce the linear subspace H-F(p) of H consisting of elements whose frame coefficient sequences belong to the l(p)-space, where 1 \u3c = p \u3c 2. Our focus is on the general theory of these spaces, and we investigate different aspects of these spaces in relation to reconstructions, p-frames, realizations and dilations. In particular we show that for closed linear subspaces of H, only finite dimensional ones can be realized as H-F(p)-spaces for some frame F. We also prove that with a mild decay condition on the frame F the frame expansion of any element in H-F(p) converges in both the Hilbert space norm and the parallel to . parallel to(F, p-) norm which is induced by the l(p)-norm