## Orderings and non-formal deformation quantization.(English)Zbl 1136.53064

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.

### MSC:

 53D55 Deformation quantization, star products 46L65 Quantizations, deformations for selfadjoint operator algebras 81S10 Geometry and quantization, symplectic methods
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### References:

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