Abstract
1. In this note we first generalize a result of P. R. Halmos [3 ] concerning commutators of (bounded) operators on Hilbert space. Then we obtain some partial results on a problem of commutators in von Neumann algebras which is closely related to another problem raised by Halmos in [4]. Let 3C be any (infinite-dimensional) Hilbert space, and let ?(3C) denote the algebra of all bounded operators on EC. We follow Halmos [3] in calling a subspace 3CCEC large if SC contains infinitely many orthogonal copies of XC&XC. Halmos proved in [3] that any operator in ?(EC) with a large reducing null space is a commutator (of two bounded operators in ?(aC)). We generalize this to
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