Orderings and non-formal deformation quantization (Q2475211)

The authors study the non-formal deformation quantization of Fréchet-Poisson algebra. In the original sense, a deformation means a formal deformation of a Poisson algebra. The question of convergence naturally follows. This question has been studied later, first in the framework of \(C^*\)-algebras (by Rieffel) and then in the symplectic context (by Weinstein). Here, the authors concentrate on the deformation quantization of a Fréchet-Poisson algebra. The convergence problem as well as ordering problems are also considered. This work leads to a better understanding of star exponential functions.