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Sibirskii Matematicheskii Zhurnal, 2005, Volume 46, Number 1, Pages 32–45
(Mi smj956)
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This article is cited in 19 scientific papers (total in 19 papers)
On representation of elements of a Von Neumann algebra in the form of finite sums of products of projections
A. M. Bikchentaev N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University
Abstract:
We prove that each element of the von Neumann algebra without a direct abelian summand is representable as a finite sum of products of at most three projections in the algebra. In a properly infinite algebra the number of product terms is at most two. Our result gives a new proof of equivalence of the primary classification of von Neumann algebras in terms of projections and traces and also a description for the Jordan structure of the “algebra of observables” of quantum mechanics in terms of the “questions” of quantum mechanics.
Keywords:
$C^*$-algebra, von Neumann algebra, trace, bounded linear operator, idempotent, projection, linear span, Hilbert space.
Received: 02.04.2004
Citation:
A. M. Bikchentaev, “On representation of elements of a Von Neumann algebra in the form of finite sums of products of projections”, Sibirsk. Mat. Zh., 46:1 (2005), 32–45; Siberian Math. J., 46:1 (2005), 24–34
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https://www.mathnet.ru/eng/smj956 https://www.mathnet.ru/eng/smj/v46/i1/p32
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