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Let $\mathcal{R}$ denote the hyperfinite type $II_{1}$ factor, with $\mathcal{R}^{\omega}$ the ultrapower of $\mathcal{R}$, in respect to some ultrafilter $\omega$ on $\mathbb{N}$. I'm reading a paper and it is stated that any $x\in\mathcal{R}^{\omega}$ is the $||.||_{2}$-limit of a sequence of unitaries in $\mathcal{R}$. Unfortunately this is not completely clear for me. Can someone explain me why is this fact true ? Thank you and merry Xmas!

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