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!


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.