Abstract:

In this talk, I will present some joint work with Svea Beiser on the construction of Frechet algebras out of algebras with a countable vector space basis. The interesting examples include in particular the group algebra of $\mathbb{Z}$, polynomial algebras, infinite matrices but also several star product algebras. For the Wick star product this yields a convergent setting. As an outlook I will comment on the situation for the Wick type star product on the Poincare disc.