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    Frames of subspaces and operators

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    We study the relationship between operators, orthonormal basis of subspaces and frames of subspaces (also called fusion frames) for a separable Hilbert space H\mathcal{H}. We get sufficient conditions on an orthonormal basis of subspaces E={Ei}i∈I\mathcal{E} = \{E_i \}_{i\in I} of a Hilbert space K\mathcal{K} and a surjective T∈L(K,H)T\in L(\mathcal{K}, \mathcal{H}) in order that {T(Ei)}i∈I\{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.Comment: 21 pages, LaTeX; added references and comments about fusion frame

    Wigner function and coherence properties of cold and thermal neutrons

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    We analyze the coherence properties of a cold or a thermal neutron by utilizing the Wigner quasidistribution function. We look in particular at a recent experiment performed by Badurek {\em et al.}, in which a polarized neutron crosses a magnetic field that is orthogonal to its spin, producing highly non-classical states. The quantal coherence is extremely sensitive to the field fluctuation at high neutron momenta. A "decoherence parameter" is introduced in order to get quantitative estimates of the losses of coherence.Comment: 6 pages, 3 figures. Contribution to the Sixth Central-European Workshop on Quantum Optics, Chudobin near Olomouc, Czech Republic, April-May 199
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