Semiclassical spectral estimates for Toeplitz operators

Let X be compact Kahler manifold with integral Kahler class and L --> X a h olomorphic Hermitian line bundle whose curvature is the symplectic form of X. Let H is an element of C-infinity(X, R) be a Hamiltonian, and let T-k be the Toeplitz operator with multiplier H acting on the space H-k = H-0(X, L -xk). We obtain estimates on the eigenvalues and eigensections of T-k as k --> infinity, in terms of the classical Hamilton flow of H. We study in som e detail the case when X is an integral coadjoint orbit of a Lie group.