  We study the relationship between operators, orthonormal basis of subspaces
and frames of subspaces (also called fusion frames) for a separable Hilbert
space $\mathcal{H}$. We get sufficient conditions on an orthonormal basis of
subspaces $\mathcal{E} = \{E_i \}_{i\in I}$ of a Hilbert space $\mathcal{K}$
and a surjective $T\in L(\mathcal{K}, \mathcal{H})$ 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 related frames of
subspaces (including the computation of their weights) and oblique projections.
The notion of refinament 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.
