Berezin–Toeplitz quantization and composition formulas

Extending results in [L.A. Coburn, The measure algebra of the Heisenberg group, J. Funct. Anal. 161 (1999) 509–525; L.A. Coburn, On the Berezin–Toeplitz calculus, Proc. Amer. Math. Soc. 129 (11) (2001) 3331–3338] we derive composition formulas for Berezin–Toeplitz operators with i.g. unbounded symbols in the range of certain integral transforms. The question whether a finite product of Berezin–Toeplitz operators is an operator of this type again can be answered affirmatively in several cases, but there are also well-known counter examples. We explain some consequences of such formulas to C∗-algebras generated by Toeplitz operators. © 2008 Published by Elsevier Inc.