  Operator-valued frames (or g-frames) are generalizations of frames and fusion
frames and have been used in packets encoding, quantum computing, theory of
coherent states and more.
  In this paper, we give a new formula for operator-valued frames for finite
dimensional Hilbert spaces. As an application, we derive in a simple manner a
recent result of A. Najati concerning the approximation of g-frames by Parseval
ones. We obtain also some results concerning the best approximation of
operator-valued frames by its alternate duals, with optimal estimates.
