Geodesic
Multiplicative Commutators of Operators
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 737-749

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

An invertible operator T on a Hilbert space is a multiplicative commutator if there exist invertible operators A and B on such that T = ABA–1B–1. In this paper we discuss the question of which operators are, and which are not, multiplicative commutators. The analogous question for additive commutators (operators of the form AB — BA) has received considerable attention and has, in fact, been completely settled (2). The present results represent the information we have been able to obtain by carrying over to the multiplicative problem the techniques that proved efficacious in the additive situation. While these results remain incomplete, they suffice, for example, to enable us to determine precisely which normal operators are multiplicative commutators. 
Brown, Arlen; Pearcy, Carl. Multiplicative Commutators of Operators. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 737-749. doi: 10.4153/CJM-1966-074-1
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[1] 1. Brown, A., Halmos, P. R., and Pearcy, C., Commutators of operators on Hilbert space, Can. J. Math., 17 (1965), 695–708. Google Scholar

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