# WOT continuity

suppose $\varphi$ is a linear functional on $B(H)$. Show that if there exists vectors $x_1,\dots,x_{n}$ and $y_1,\dots,y_2$ in $H$ such that $\varphi(T)=\sum^{n}_{k=1}\langle Tx_k,y_k\rangle$ with $T\in B(H)$ then $\varphi$ is WOT continuous.