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Rings of Quotients of Finite AW ∗-Algebras: Representation and Algebraic Approximation

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Algebra and Logic Aims and scope

We show that Berberian’s ∗-regular extension of a finite AW ∗-algebra admits a faithful representation, matching the involution with adjunction, in the ℂ-algebra of endomorphisms of a closed subspace of some ultrapower of a Hilbert space. It also turns out that this extension is a homomorphic image of a regular subalgebra of an ultraproduct of matrix ∗-algebras ℂn×n.

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Darmstadt, Schloβgartenstr. 7, Darmstadt, 64289, Germany

    C. Herrmann

  2. Sobolev Institute ofMathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    M. V. Semenova

  3. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    M. V. Semenova

Authors
  1. C. Herrmann
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  2. M. V. Semenova
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Correspondence to M. V. Semenova.

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*Supported by the Grants Council (under RF President) for State Aid of Young Doctors of Science (project MD-2587.2010.1), by the J. Mianowski Fund, and by the Fund for Polish Science.

Translated from Algebra i Logika, Vol. 53, No. 4, pp. 466-504, July-August, 2014.

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Herrmann, C., Semenova, M.V. Rings of Quotients of Finite AW ∗-Algebras: Representation and Algebraic Approximation. Algebra Logic 53, 298–322 (2014). https://doi.org/10.1007/s10469-014-9292-7

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  • DOI: https://doi.org/10.1007/s10469-014-9292-7

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