Semi-classical properties of Berezin--Toeplitz operators with $\cC^k$--\,symbol

Abstract

We obtain the semi-classical expansion of the kernels and traces of Toeplitz operators with $\cC^k$--\,symbol on a symplectic manifold. We also give a semi-classical estimate of the distance of a Toeplitz operator to the space of self-adjoint and multiplication operators.