1. Haag, R., Kastler, D.: J. Math. Phys.5, 848 (1964).
2. Schlieder, S.: Commun. Math. Phys.13, 216 (1969).
3. Rickart, Charles E.: General theory of Banach algebras. Princeton: Van Nostrand 1960.
4. Dixmier, Jaques: Les C*-algèbres et leurs représentations. Paris: Gauthier-Villars 1964.
5. The original version of the proof of lemma 1 needed the assumption that there exists a representation π of $$\mathfrak{A}$$ 12 with π( $$\mathfrak{A}$$ 1)″ and π( $$\mathfrak{A}$$ 2)″ fulfilling the proposition of Schlieder. The idea of the proof given in this paper is due to Borchers.