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 $p>1$.
Categories: math.FA