Essential central range and selfadjoint commutators in properly infinite von Neumann algebras

The essential central range of an element <italic>A</italic> of a von Neumann algebra with respect to a central ideal is characterized as those elements arbitrarily close to the compression of <italic>A</italic> to a subspace large with respect to the ideal. The selfadjoint commutators in a properly infinite algebra are shown to be the elements whose essential central ranges with respect to the strong radical contain 0.

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