Weighted projections and Riesz frames

J. ANTEZANA, G. CORACH, M. RUIZ Y D. STOJANOFF

LINEAR ALGEBRA AND ITS APPLICATIONS

Birkhauser

Año: 2005 vol. 402 p. 367 - 389

0024-3795

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.