On Commutators of Operators on Hilbert Space
نویسنده
چکیده
1. In this note we first generalize a result of P. R. Halmos [3] concerning commutators of (bounded ) operators on Hubert 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) Hubert space, and let £(3C) denote the algebra of all bounded operators on 3C. We follow Halmos [3] in calling a subspace 3CC3C large if X contains infinitely many orthogonal copies of 3C03C. Halmos proved in [3] that any operator in £(3C) with a large reducing null space is a commutator (of two bounded operators in £(3C)). We generalize this to
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تاریخ انتشار 2010