On the Berezin-Toeplitz calculus

We consider the problem of composing Berezin-Toeplitz operators on the Hilbert space of Gaussian square-integrable entire functions on complex n-space, C-n. For several interesting algebras of functions on C-n, we have TphiTpsi = T-phi lozenge psi for all phi,psi in the algebra, where T-phi is the Berezin-Toeplitz operator associated with phi and phi lozenge psi is a "twisted" associative product on the algebra of functions. On the other hand, there is a C-infinity function phi for which T-phi is bounded but T(phi)T(phi)not equalT(psi) for any psi.