Is $A\mapsto \operatorname{tr}( A \rho)$ WOT continuous?

Question

Let $\rho$ be a nonnegative linear operator on a Hilbert space $H$ with $\operatorname{tr}(\rho)=1$. Then is $A\mapsto \operatorname{tr}( A \rho)$ WOT continuous on the space of bounded linear operators $L(H)$?

EDIT:

• By WOT, I mean weak operator topology.
• I can prove that $A\mapsto \operatorname{tr}( A \rho)$ is sequentially WOT-continuous. However, I can’t seem to prove WOT-continuity