Landau-Hall States and Berezin-Toeplitz Quantization of Matrix Algebras

We argue that the Landau-Hall states provide a suitable framework for formulating the Berezin-Toeplitz quantization of classical functions on a K"ahler phase space. We derive the star-products for such functions in this framework and generalize the Berezin-Toeplitz quantization to matrix-valued classical functions. We also comment on how this is related to different calculations of the effective action for Hall systems.