Schatten Class Operators in a Representation Space of Canonical Commutation Relations

The Schatten classes $\mathfrak S_p$ of operators in a Hilbert space—a noncommutative analog of the classical $l_p$ spaces—play a significant role in recent studies on quantum information theory. In the present paper we give sufficient conditions for an operator to belong to $\mathfrak S_p$ in the case where the Hilbert space is the space of an irreducible representation of the canonical commutation relations.