Some properties of frames of subspaces obtained by operator theory methods

M. A. RUIZ Y D. STOJANOFF

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Elsevier

Año: 2007

0022-247X

We study the relationship among operators, orthonormal basis of subspaces and frames of subspaces (also called fusion frames) for a separable Hilbert space H. We get sufficient conditions on an orthonormal basis of subspaces E = {E_i }_{i\in I} of a Hilbert space K and  a surjective T \in L(K , H ) in order  that {T(E_i)}_{i\in I} is a frame of subspaces with respect to a computable sequence of weights. We also obtain generalizations of  results in [J. A. Antezana, G. Corach, M. Ruiz and D. Stojanoff,  Oblique projections and frames. Proc. Amer. Math. Soc.  134  (2006), 1031-1037],  which relate frames of subspaces (including the computation of their weights) and oblique projections. The notion of refinement of a fusion frame  is defined and used to obtain results about the excess of such frames. We study the set of admissible weights for a generating sequence of subspaces. Several examples are given.