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In this paper we study the fusion frame potential, that is a generalization of the Benedetto-Fickus (vectorial) frame potential to the finite-dimensional fusion frame setting. The structure of local and global minimizers of this potential is studied, when we restrict the frame potential to suitable sets of fusion frames. These minimizers are related to… (More)

We present results about minimization of convex functionals defined over a finite set of vectors in a finite dimensional Hilbert space, that extend several known results for the Benedetto-Fickus frame potential. Our approach depends on majorization techniques. We also consider some perturbation problems, where a positive perturbation of the frame operator… (More)

Given a finite sequence of vectors F 0 in C d we describe the spectral and geometrical structure of optimal frame completions of F 0 obtained by appending a finite sequence of vectors with prescribed norms, where optimality is measured with respect to a general convex potential. In particular, our analysis includes the so-called Mean Square Error (MSE) and… (More)

This work aimed to develop a new therapeutic approach to increase the efficacy of 5-fluorouracil (5-FU) in the treatment of advanced or recurrent colon cancer. 5-FU-loaded biodegradable poly(ε-caprolactone) nanoparticles (PCL NPs) were combined with the cytotoxic suicide gene E (combined therapy). The SW480 human cancer cell line was used to assay the… (More)

Given a finite sequence of vectors F 0 in C d we describe the spectral and geometrical structure of optimal completions of F 0 obtained by adding a finite sequence of vectors with prescribed norms, where optimality is measured with respect to a general convex potential. In particular, our analysis includes the so-called Mean Square Error (MSE) and the… (More)

We study the relationship between 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 = {E i } i∈I of a Hilbert space K and a surjective T ∈ L(K, H) in order that {T (E i)} i∈I is a frame of subspaces with respect to… (More)

In this paper we study the fusion frame potential, that is a generalization of the Benedetto-Fickus (vectorial) frame potential to the finite-dimensional fusion frame setting. Local and global minimizers of this potential are studied, when we restrict it to a suitable set of fusion frames. These minimizers are related to tight fusion frames as in the… (More)

Let H be a (separable) Hilbert space and {e k } k≥1 a fixed orthonormal basis of H. Motivated by many papers on scaled projections, angles of subspaces and oblique projections, we define and study the notion of compatibility between a subspace and the abelian algebra of diagonal operators in the given basis. This is used to refine previous work on scaled… (More)

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