Geodesic
On Products of Symmetries
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 897-900

Voir la notice de l'article provenant de la source Cambridge University Press

In (2) Halmos and Kakutani proved that any unitary operator on an infinite-dimensional Hilbert space is a product of at most four symmetries (self-adjoint unitaries). It is the purpose of this paper to show that if the unitary is an element of a properly infinite von Neumann algebra A (i.e., one with no finite non-zero central projections), then the symmetries may be chosen from A. A principal tool used in establishing this result is Theorem 1, which was proved by Murray and von Neumann (6, 3.2.3) for type II1 factors; see also (3, Lemma 5). The author would like to thank David Topping for raising the question, and for several stimulating conversations on the subject. He is also indebted to the referee for several helpful suggestions. 
Fillmore, Peter A. On Products of Symmetries. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 897-900. doi: 10.4153/CJM-1966-090-5
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