Commutators in Factors of Type III
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1152-1160
Voir la notice de l'article provenant de la source Cambridge University Press
Let denote a separable, complex Hilbert space, and let R be a von Neumann algebra acting on . (A von Neumann algebra is a weakly closed, self-adjoint algebra of operators that contains the identity operator on its underlying space.) An element A of R is a commutator in R if there exist operators B and C in R such that A = BC — CB. The problem of specifying exactly which operators are commutators in R has been solved in certain special cases; e.g. if R is an algebra of type In (n < ∞) (2), and if R is a factor of type I∞ (1). It is the purpose of this note to treat the same problem in case R is a factor of type III. Our main result is the following theorem.
Brown, Arlen; Pearcy, Carl. Commutators in Factors of Type III. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1152-1160. doi: 10.4153/CJM-1966-115-2
@article{10_4153_CJM_1966_115_2,
author = {Brown, Arlen and Pearcy, Carl},
title = {Commutators in {Factors} of {Type} {III}},
journal = {Canadian journal of mathematics},
pages = {1152--1160},
year = {1966},
volume = {18},
number = {1},
doi = {10.4153/CJM-1966-115-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-115-2/}
}
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