## Independence of local algebras in quantum field theory.(English)Zbl 0197.26303

quantum theory
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 [1] Haag, R., Kastler, D.: J. Math. Phys.5, 848 (1964). · Zbl 0139.46003 [2] Schlieder, S.: Commun. Math. Phys.13, 216 (1969). · Zbl 0179.58001 [3] Rickart, Charles E.: General theory of Banach algebras. Princeton: Van Nostrand 1960. · Zbl 0095.09702 [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 {$$\pi$$} of $$\mathfrak{A}$$ 12 with {$$\pi$$}( $$\mathfrak{A}$$ 1)” and {$$\pi$$}( $$\mathfrak{A}$$ 2)” fulfilling the proposition of Schlieder. The idea of the proof given in this paper is due to Borchers. [6] Turumaru, T.: Tôhoku Math. J.8, 281 (1956). · Zbl 0072.32903 [7] —- Tôhoku Math. J.16, 111 (1964). · Zbl 0127.07302 [8] Wulfsohn, A.: Bull. Sci. Math.87, 13 (1963). [9] Okayasu, T.: Tôhoku Math. J.18, 325 (1966). · Zbl 0152.33101
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