Commutators of Hilbert-Schmidt operators. I
It is known that if D is a diagonal matrix with entries \(d,d_ 1,d_ 2,..\). where \(d_ n\downarrow 0\), \(\sum d_ n=d\), and if D is a finite sum of commutators of Hilbert-Schmidt operators, then \(\sum (\log n)d_ n<\infty\). In this paper the converse is proved providing a complete characterization of this class of Hilbert-Schmidt commutators and settling in the negative the related 1971 problem of Pearcy and Topping.
finite sum of commutators of Hilbert-Schmidt operators
scientific article; zbMATH DE number 4002874