TOEPLITZ QUANTIZATION OF KAHLER-MANIFOLDS AND GL(N), N-]INFINITY LIMITS

For general compact Kahler manifolds it is shown that both Toeplitz quantization and geometric quantization lead to a well-defined (by operator norm estimates) classical limit. This generalizes earlier results of the authors and Klimek and Lesniewki obtained for the torus and higher genus Riemann surfaces, respectively. We thereby arrive at an approximation of the Poisson algebra by a sequence of finite-dimensional matrix algebras gl(N), N --> infinity.