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Zeitschrift für Analysis und ihre Anwendungen

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Volume 4, Issue 4, 1985, pp. 363–372
DOI: 10.4171/ZAA/159

Published online: 1985-08-31

Twistprodukt und Quasi-*-AIgebren

Gerd Lassner[1] and Gisela A. Lassner[2]

(1) Universität Leipzig, Germany
(2) Universität Leipzig, Germany

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.

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Lassner Gerd, Lassner Gisela: Twistprodukt und Quasi-*-AIgebren. Z. Anal. Anwend. 4 (1985), 363-372. doi: 10.4171/ZAA/159