Discrete Translates of an Operator in the Schatten $p$-Classes

Bhawna Dharra, S. Sivananthan, D. Venku Naidu

Published 2023-11-28Version 1

In this manuscript, we investigate the properties of systems formed by translations of an operator in the Schatten $p$-classes $\mathcal{T}^p$. We establish the existence of Schauder frames of integer translates in $\mathcal{T}^p$ for $p>2$. Later, we provide an instance of a uniformly discrete $\Lambda \subset \mathbb{R}^{2d}$ such that there exists an operator whose $\Lambda$-translates are complete in $\mathcal{T}^p$ for all $p>1$.