Weighted projections and Riesz frames

2004/11/15 by Jorge Antezana, Antezana, Jorge, Gustavo Corach +5
Computer Science · Mathematics · #47A30 (Primary) #47B15 (Secondary) #Digital Filter Design and Implementation #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.math/0411326

openalex publication_date 2004/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 projections, and to obtain a new characterization of Riesz frames.

Citations

• Continuous and Discrete Wavelet Transforms
• Oblique projections and Schur complements

Related

• Frames of subspaces and operators
• Every frame is a sum of three (but nottwo) orthonormal bases, and other frame representations
• Riesz bases from orthonormal bases by replacement
• G-frames and G-Riesz Bases
• Characterizing Hilbert space frames with the subframe property