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Semi-classical properties of Berezin–Toeplitz operators with $\mathscr {C}^k$Ck-symbol
We obtain the semi-classical expansion of the kernels and traces of Toeplitz operators with \documentclass[12pt]{minimal}\begin{document}$\mathscr {C}^k$\end{document}Ck-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.