  In the Reflection Positivity theory and its application to statistical
mechanical systems, certain matrix inequalities play a central role. The
Dyson-Lieb-Simon and Kennedy-Lieb-Shastry-Schupp inequalities constitute
prominent examples. In this paper we extend the KLS-S inequality to the case
where matrices are replaced by certain operators. As an application, we prove
the occurrence of the long range order in the ground state of two-dimensional
quantum rotors.
