Berezin-Toeplitz quantization and Berezin symbols for arbitrary compact Kähler manifolds

For phase-space manifolds which are compact Kähler manifolds relations between the Berezin-Toeplitz quantization and the quantization with the help of Berezin's coherent states and symbols are studied. First the results on the Berezin-Toeplitz quantization of arbitrary compact Kähler manifolds due to Bordemann, Meinrenken and Schlichenmaier are recalled. It is shown that the covariant symbol map is adjoint to the Toeplitz map. The Berezin transform for compact Kähler manifolds is discussed