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This article is cited in 6 scientific papers (total in 6 papers)
Rings of quotients of finite $AW^*$-algebras. Representation and algebraic approximation
C. Herrmanna, M. V. Semenovabc a Fachbereich Mathematik, Technische Universität Darmstadt, Schloßgartenstr. 7, Darmstadt, 64289, Germany
b Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
c Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia
Abstract:
We show that Berberian's $*$-regular extension of a finite $AW^*$-algebra admits a faithful representation, matching the involution with adjunction, in the $\mathbb C$-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 $\mathbb C^{n\times n}$.
Keywords:
$AW^*$-algebra, finite Rickart $C^*$-algebra, ring of quotients, $*$-regular ring, projection ortholattice, ultraproduct.
Received: 28.07.2013 Revised: 14.08.2014
Citation:
C. Herrmann, M. V. Semenova, “Rings of quotients of finite $AW^*$-algebras. Representation and algebraic approximation”, Algebra Logika, 53:4 (2014), 466–504; Algebra and Logic, 53:4 (2014), 298–322
Linking options:
https://www.mathnet.ru/eng/al646 https://www.mathnet.ru/eng/al/v53/i4/p466
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