Perturbations of Subalgebras of Type ${\mathrm{II}}_1$ Factors

Sorin Popa, Allan Sinclair, Roger Smith

We consider two von Neumann subalgebras $\cl B_0$ and $\cl B$ of a type ${\mathrm{II}}_1$ factor $\cl N$. For a map $\varphi$ on $\cl N$, we define \[\|ϕ\|_{\infty,2}=\sup\{\|ϕ(x)\|_2\colon…