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Sbornik: Mathematics, 2008, Volume 199, Issue 4, Pages 477–493
DOI: https://doi.org/10.1070/SM2008v199n04ABEH003929 (Mi sm3851) 		 
This article is cited in 12 scientific papers (total in 12 papers)

On the representation of elements of a von Neumann algebra in the form of finite sums of products of projections. III. Commutators in $C^*$-algebras

A. M. Bikchentaev

N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University
English version PDF (369 kB) Citations (12)
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DOI: https://doi.org/10.1070/SM2008v199n04ABEH003929
Abstract: It is proved that every skew-Hermitian element of any properly infinite von Neumann algebra can be represented in the form of a finite sum of commutators of projections in this algebra. A new commutation condition for projections in terms of their upper (lower) bound in the lattice of all projections of the algebra is obtained. For the full matrix algebra the set of operators with canonical trace zero is described in terms of finite sums of commutators of projections and the domain in which the trace is positive is described in terms of finite sums of pairwise products of projections. Applications to $AF$-algebras are obtained.
Bibliography: 33 titles.
Received: 12.03.2007 and 24.10.2007
Russian version:
Matematicheskii Sbornik, 2008, Volume 199, Number 4, Pages 3–20
DOI: https://doi.org/10.4213/sm3851
Bibliographic databases:
UDC: 517.983+517.987
MSC: Primary 46L10; Secondary 47C15
Language: English
Original paper language: Russian
Citation: A. M. Bikchentaev, “On the representation of elements of a von Neumann algebra in the form of finite sums of products of projections. III. Commutators in $C^*$-algebras”, Mat. Sb., 199:4 (2008), 3–20; Sb. Math., 199:4 (2008), 477–493
Citation in format AMSBIB
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