Abstract
Let M be a factor von Neumann algebra with separable predual and let T∈M. We call T an irreducible operator (relative to M) if W⁎(T) is an irreducible subfactor of M, i.e., W⁎(T)′∩M=CI. In this note, we show that the set of irreducible operators in M is a dense Gδ subset of M in the operator norm. This is a natural generalization of a theorem of Halmos.
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