LINEAR INDEPENDENCE OF QUANTUM TRANSLATES

Abstract If A is in the p -Schatten class on ${\mathbb {R}}^n$ , $1\leq p \leq {4n}/{(2n-1)}$ , then the quantum translates of A are linearly independent. Moreover, there exists a nonzero operator in the p -Schatten class on ${\mathbb {R}}^n$ , $p>{4n}/{(2n-1)}$ , whose quantum translates are linearly dependent.