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Weighted projections and Riesz frames

Jorge Antezana·Gustavo Corach·Mariano Ruiz·Demetrio Stojanoff
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Abstract

Let $\mathcal{H}$ be a (separable) Hilbert space and $\{e_k\}_{k\geq 1}$ a fixed orthonormal basis of $\mathcal{H}$. 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 projections, and to obtain a new characterization of Riesz frames.

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Jorge Antezana, Gustavo Corach, Mariano Ruiz, Demetrio Stojanoff. 2004-11-15. Weighted projections and Riesz frames. https://arxiv.org/abs/math/0411326

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