SUPER TOEPLITZ-OPERATORS AND NONPERTURBATIVE DEFORMATION QUANTIZATIONOF SUPERMANIFOLDS

The purpose of this paper is to construct non-perturbative deformation quantizations of the algebras of smooth functions on Poisson superman ifolds. For the examples U1\1 and C(m\n), algebras of super Toeplitz o perators are defined with respect to certain Hilbert spaces of superho lomorphic functions. Generators and relations for these algebras are g iven. The algebras can be thought of as algebras of ''quantized functi ons,'' and deformation conditions are proven which demonstrate the rec overy of the super Poisson structures in a semi-classical limit.