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: 2008 vol. 343 p. 366 - 378

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 = {Ei }i∈I of a Hilbert space K and a surjective T ∈ L(K,H) in order that {T (Ei )}i∈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, 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. © 2008 Elsevier Inc. All rights reserved.