Weakly Separated Bessel Systems of Model Spaces

TL;DR

This paper proves that weakly separated Bessel systems of model spaces in the Hardy space are Riesz systems, with implications for matrix interpolation sequences, without relying on the Feichtinger conjecture solution.

Contribution

It establishes a new characterization of weakly separated Bessel systems as Riesz systems in the Hardy space, avoiding recent conjecture solutions.

Findings

Weakly separated Bessel systems are Riesz systems.

Applications to interpolating sequences of matrices.

The Feichtinger conjecture approach does not extend to multi-dimensional model sub-spaces.

Abstract

We show that any weakly separated Bessel system of model spaces in the Hardy space on the unit disc is a Riesz system and we highlight some applications to interpolating sequences of matrices. This will be done without using the recent solution of the Feichtinger conjecture, whose natural generalization to multi-dimensional model sub-spaces of $\mathrm{H}^2$ turns out to be false.