Berezin--Toeplitz quantization and invariant symbolic calculi (Q1417861)

The author describes a way to obtain, on bounded symmetric domains, all the G-invariant star products, which are equivalent to the Berezin-Toeplitz star-products. To quantize Kähler manifolds, the star product used is the Berezin-Toeplitz star product. Expanding the product of two Toeplitz operators asymptotically into a new series; one can often construct an invariant star product. In this paper, instead of using Toeplitz operators, the author considers suitable mappings. The procedure in question is called ``prime quantization'' by some authors. Two technical results are then proved. The first is in some sense a generalization of a theorem of Borel. The second is the fact that any Hochschild two-cochains on a bounded symmetric comain maps the Schwartz space to itself.