Some properties of frames of subspaces obtained by operator theory methods |
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Authors: | Mariano A. Ruiz Demetrio Stojanoff |
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Affiliation: | a Departamento de Matemática, FCE-UNLP, La Plata, Argentina b IAM-CONICET, Saavedra 15, Piso 3 (1083), Buenos Aires, Argentina |
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Abstract: | 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. |
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Keywords: | Frames Frames of subspaces Fusion frames Hilbert space operators Oblique projections |
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