Weighted projections and Riesz frames

Jorge Antezana; Gustavo Corach; Mariano Ruiz; Demetrio Stojanoff

Weighted projections and Riesz frames

Functional Analysis 2007-05-23 v1 Numerical Analysis

Authors: Jorge Antezana , Gustavo Corach , Mariano Ruiz , Demetrio Stojanoff

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.

Keywords

frame theory projective geometry operator theory on hilbert spaces

Cite

@article{arxiv.math/0411326,
  title  = {Weighted projections and Riesz frames},
  author = {Jorge Antezana and Gustavo Corach and Mariano Ruiz and Demetrio Stojanoff},
  journal= {arXiv preprint arXiv:math/0411326},
  year   = {2007}
}

Comments

23 pages, to appear in Linear Algebra and its Applications

Weighted projections and Riesz frames

Abstract

Keywords

Cite

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