Hello,

Is there a counterexample to the following statement: let $A,B$ two von Neumann algebras, every morphism $A \rightarrow B$ of $C^* $-algebras is a $W^*$-homomorphism ?

( a $W^* $-homomorphism is a continuous morphism for the weak topologies $\sigma(A,A_* )$ and $\sigma(B,B_* )$, where $A_* $ and $B_* $ are the preduals)

Thanks in advance.