Weighted projections and Riesz frames Original Research Article

Let image be a (separable) Hilbert space and {ek}kgreater-or-equal, slanted1 a fixed orthonormal basis of image. 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.