The commutant modulo the set of compact operators of a von Neumann algebra (Q1095350)

Let B(H) be the algebra of bounded operators on a Hilbert space H and let K(H)\(\subset B(H)\) be the ideal of compact operators on H. One of the interesting results the author proves is: Let M be a von Neumann algebra acting on the Hilbert space H. If T is an operator on H such that Tx-xT\(\in K(H)\) for all \(x\in M\) then there exists \(T\in M'\) such that T-T'\(\in K(H)\). Here T' and M' are the commutants of T and M, respectively.