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On Partially Ordered Real Involutory Algebras

Albeverio, S. ; Ayupov, Sh ; Dadakhodjayev, R.

In: Acta Applicandae Mathematica, 2006, vol. 94, no. 3, p. 195-214

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    Titel
    • On Partially Ordered Real Involutory Algebras
    Autor
    • Albeverio, S.. Institut für Angewandte Mathematik, Universität Bonn, Wegelerstr. 6, 53115, Bonn, Germany
    • Ayupov, Sh. Institute of Mathematics, Uzbekistan Academy of Science, F. Hodjaev str. 29, 700143, Tashkent, Uzbekistan
    • Dadakhodjayev, R.. Institute of Mathematics, Uzbekistan Academy of Science, F. Hodjaev str. 29, 700143, Tashkent, Uzbekistan
    Dokumententyp
    • Postprint
    Sprache
    • Englisch
    Veröffentlicht in
    • Acta Applicandae Mathematica, 2006, vol. 94, no. 3, p. 195-214. Springer Netherlands
    Andere elektronische Ausgabe
    OAI-PMH-ID
    • oai:doc.rero.ch:319079
    Summary
    In this paper we study real O *-algebra, on the hermitian elements of which a partial order exists which is compatible with the algebraic structure. Such algebras occur in the axiomatic approach to the description of the space of random variables (observables) in quantum probability theory. We study the relations between these so called real O *-algebras and their complexification, and also their Jordan structure. Our main result is the theorem on the representation of abstract real O *-algebras as algebras of locally measurable (unbounded) operators affiliated with a real von Neumann algebra on a Hilbert space