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.

(I'm missing something elementary...)