Weighted projections and Riesz frames

Details Weighted projections and Riesz frames Weighted projections and Riesz frames

2004-11-15

arxiv.org/abs/math/0411326v1

Mathematics

Functional Analysis

23 pages, to appear in Linear Algebra and its Applications

Scientific paper

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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