
Journal of Lie Theory 15 (2005), No. 1, 027050 Copyright Heldermann Verlag 2005 BerezinToeplitz Quantization on the Schwartz Space of Bounded Symmetric Domains Miroslav Englis Mathematical Institute, Czech Academy of Sciences, Zitna 25, 11567 Praha 1, Czech Republic englis@math.cas.cz Borthwick, Lesniewski and Upmeier [Nonperturbative deformation quantization of Cartan domains, J. Funct. Anal. 113 (1993) 153176] proved that on any bounded symmetric domain (Hermitian symmetric space of noncompact type), for any compactly supported smooth functions f and g, the product of the Toeplitz operators T_{f}T_{g} on the standard weighted Bergman spaces can be asymptotically expanded into a series of another Toeplitz operators multiplied by decreasing powers of the Wallach parameter ν. This is the BerezinToeplitz quantization. We remove the hypothesis of compact support and show that their result can be extended to functions f, g in a certain algebra which contains both the space of all smooth functions whose derivatives of all orders are bounded and the Schwartz space. Applications to deformation quantization are also given. Keywords: BerezinToeplitz quantization, bounded symmetric domain, Schwartz space. MSC: 22E30; 43A85, 47B35, 53D55 [ Fulltextpdf (264 KB)] for subscribers only. 