Let $(A,H)$ be a von Neumann algebra in standard form (which means that $H=L^2A$), and recall that the automorphism group $Aut(A)$ acts on both $A$ and $H$. Let $$N:=\{u\in U(H): uAu^*=A\}$$ be the normalizer of $A$, equipped with the strong topoloy (the subspace topology from $U(H)$). The group $N$ is canonically isomorphic to the semidirect product $$N\cong Aut(A)\ltimes U(A').$$

Equip $Aut(A)$ with Haagerup's *u*-topology, i.e. the topology of pointwise convergence on $A_*$, equivlalently, it is the topology of pointwise convergence on $H$.

** Question:** is the projection map $$N\to Aut(A)$$ continuous?