Some properties of frames of subspaces obtained by operator theory methods

• Autores: Ruiz, Mariano Andrés; Stojanoff, Demetrio
• Año de publicación: 2008
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Matemática; Frames; Frames of subspaces; Fusion frames; Hilbert space operators; Oblique projections
• Institución: Universidad Nacional de La Plata

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.
Facultad de Ciencias Exactas