Geodesic
Operators of the form PAQ-QAP
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1353-1361

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

In this note the Hilbert spaces under consideration are complex, and the operators referred to are bounded, linear operators. If is a Hilbert space, then the algebra of all operators on is denoted by .It is known (1) that if is any Hilbert space, then the class of commutators on , i.e., the class of all operators that can be written in the form PQ — QP for some , can be exactly described. A similar problem is that of characterizing all operators on that can be written in the form for some . 
Brown, Arlen; Pearcy, Carl. Operators of the form PAQ-QAP. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1353-1361. doi: 10.4153/CJM-1968-135-8
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[1] 1. Brown, A. and Pearcy, C., Structure of commutators of operators, Ann. of Math. (2) 82 (1965), 112–127. Google Scholar

[2] 2. Brown, A., Halmos, P. R., and Pearcy, C., Commutators of operators on Hilbert space, Can. J. Math. 17 (1965), 695–708. Google Scholar

[3] 3. Lumer, G. and Rosenblum, M., Linear operator equations, Proc. Amer. Math. Soc. 10 (1959), 32–41. Google Scholar

[4] 4. Taussky, O., Generalized commutators of matrices and permutations of factors in a product of three matrices (Studies in Mathematics and Mechanics presented to Richard von Mises, Academic Press, New York, 1954). Google Scholar

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