Twistprodukt und Quasi-*-AIgebren

Abstract

The Schwartz distribution space $\mathcal{S}’$ becomes a topological quasi-*-algebra with the distinguished subspace $\mathcal{S}$, if one defines the so-called twisted product in it. In the paper it is pointed out that the Weyl quantization $f\to W(f)$ IV(/) is an isomorphism of this topological quasi-*-algebra onto the topological quasi-*-algebra $\mathcal{L}(\mathcal{S},\mathcal{S}’)$ of all linear continuous operators of $\mathcal{S}$ in $\mathcal{S}’$. Furthermore, the problem of the extensions of the multiplications in these quasi-*-algebras is discussed.