  Let L^k be a high power of a hermitian holomorphic line bundle over a complex
manifold X. Given a differential form f on X, we define a super Toeplitz
operator T(f) acting on the space of harmonic (0,q)-forms with values in L^k,
with symbol f. The asymptotic distribution of its eigenvalues, when k tends to
infinity, is obtained in terms of the symbol of the operator and the curvature
of the line bundle L, given certain conditions on the curvature. For example,
already when q=0 this generalizes a result of Boutet de Monvel and Guillemin to
semi-positive line bundles. The asymptotics are obtained from the asymptotics
of the Bergman kernels of the corresponding harmonic spaces. Applications to
sampling are also given.
