Published online by Cambridge University Press: 20 November 2018
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 .
This research was supported in part by the National Science Foundation. At the time the paper was written, the second author was an Alfred P. Sloan Research Fellow.