Commutators of orthogonal projections (Q1772546)

Let \(H\) be a separable complex Hilbert space and \(B(H)\) be the algebra of all bounded linear operators on \(H\). An operator \(C\in B(H)\) is said to be a commutator of operators if \(C=AB-BA\) for some \(A,\, B\in B(H)\). In this paper, the author proves that an operator \(T\) is a commutator of orthogonal projections if and only if \(T^\ast=-T\), \(\| T\| \leq 1/2\), and \(T\) is unitary equivalent to \(T^\ast\).