  Let $\mathcal M$ be a factor von Neumann algebra with separable predual and
let $T\in \mathcal M$. We call $T$ an irreducible operator (relative to
$\mathcal M$) if $W^*(T)$ is an irreducible subfactor of $\mathcal M$, i.e.,
$W^*(T)'\cap \mathcal M={\mathbb C} I$. In this note, we show that the set of
irreducible operators in $\mathcal M$ is a dense $G_\delta$ subset of $\mathcal
M$ in the operator norm. This is a natural generalization of a theorem of
Halmos.
