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Die struktur endlicher schwach abgeschlossener Jordanalgebren Teil II. Diskrete Jordanalgebren

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Abstract

In the preceding note [6] we reduced the study of continuous finite weakly closed Jordan algebras to real associative W*-algebras of type II1. Here we treat the remaining case of discrete finite weakly closed Jordan algebras and describe them completely by finite dimensional simple formally real Jordan algebras and by simple formally real Jordan algebras of quadratic forms of real Hilbert spaces. Jacobsons theory of Jordan algebras with minimum condition combined with W*-algebra techniques constitutes an essential tool in the proof.

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Literatur

  1. Alfsen, E.: Compact Convex Sets and Boundary Integrals. Erg. der Math.57. Berlin-Heidelberg-New York: Springer 1970.

    Google Scholar 

  2. Braun, H. und Koecher, M.: Jordan-Algebren. Berlin-Heidelberg-New York: Springer 1966.

    Google Scholar 

  3. Dixmier, J.: Les algèbres d'opérateurs dans l'espace Hilbertien. 2-ième ed. Paris: Gauthier-Villars 1969.

    Google Scholar 

  4. Jacobson, N.: Structure and Representations of Jordan Algebras. AMS Coll. Publ.39, Providence 1968.

    Google Scholar 

  5. Janssen, G.: Reelle Jordanalgebren mit endlicher Spur. Manuscripta Math.13, 237–273 (1974).

    Google Scholar 

  6. -: Die Struktur endlicher schwach abgeschlossener Jordanalgebren. Teil I. Stetige Jordanalgebren. Erscheint in Manuscripta Mathematica.

  7. Rickart, Ch.E.: General Theory of Banach Algebras. New York: D. van Nostrand 1960.

    Google Scholar 

  8. Riesz, F. und Sz.-Nagy, B.: Vorlesungen über Funktionalanalysis. Berlin: Deutscher Verlag der Wissenschaften 1956.

    Google Scholar 

  9. Sakai, S.: C*-Algebras and W*-Algebras. Erg. der Math.60. Berlin-Heidelberg-New York: Springer 1971.

    Google Scholar 

  10. Topping, D. M.: Jordan Algebras of Selfadjoint Operators. Mem. AMS53, Providence 1965.

    Google Scholar 

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Authors and Affiliations

  1. Institut A für Mathematik der T.U. Braunschweig, Pockelsstr. 14, 33 Braunschweig, W.-Deutschland

    Gerhard Janssen

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  1. Gerhard Janssen
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Janssen, G. Die struktur endlicher schwach abgeschlossener Jordanalgebren Teil II. Diskrete Jordanalgebren. Manuscripta Math 16, 307–332 (1975). https://doi.org/10.1007/BF01323463

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  • DOI: https://doi.org/10.1007/BF01323463

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